Week 1
Discount factor Z(t,T) provides the term of exchange between a given amount of money provides provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money term provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money exchange provides the term of exchange between a given amount of money between provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money given provides the term of exchange between a given amount of money amount provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money money provides the term of exchange between a given amount of money
at provides the term of exchange between a given amount of money t provides the term of exchange between a given amount of money versus provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money (certain) provides the term of exchange between a given amount of money amount provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money money provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money later provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money T.
Z(t,T) provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money seen provides the term of exchange between a given amount of money as provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money zero provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money $1 provides the term of exchange between a given amount of money face provides the term of exchange between a given amount of money value, provides the term of exchange between a given amount of money maturing provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money T. provides the term of exchange between a given amount of money It provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money
usually provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money case provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money market provides the term of exchange between a given amount of money participants provides the term of exchange between a given amount of money prefer provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money $1 provides the term of exchange between a given amount of money sooner provides the term of exchange between a given amount of money than provides the term of exchange between a given amount of money later, provides the term of exchange between a given amount of money hence provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money any provides the term of exchange between a given amount of money given provides the term of exchange between a given amount of money
time provides the term of exchange between a given amount of money t, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factor provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money usually provides the term of exchange between a given amount of money lower, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money longer provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money T.
Discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money are provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money constant provides the term of exchange between a given amount of money over provides the term of exchange between a given amount of money time, provides the term of exchange between a given amount of money one provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money variables provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money determines provides the term of exchange between a given amount of money this provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money
is provides the term of exchange between a given amount of money inflation:
- Higher provides the term of exchange between a given amount of money expected provides the term of exchange between a given amount of money inflation provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money money provides the term of exchange between a given amount of money less provides the term of exchange between a given amount of money valuable provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money go provides the term of exchange between a given amount of money down
Other provides the term of exchange between a given amount of money variables provides the term of exchange between a given amount of money are:
- Real provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money fluctuate
- There provides the term of exchange between a given amount of money may provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money temporary provides the term of exchange between a given amount of money liquidity provides the term of exchange between a given amount of money effects
The compounding frequency of interest accruals provides the term of exchange between a given amount of money refers provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money number provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money times provides the term of exchange between a given amount of money within provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money year
in provides the term of exchange between a given amount of money which provides the term of exchange between a given amount of money interests provides the term of exchange between a given amount of money are provides the term of exchange between a given amount of money paid provides the term of exchange between a given amount of money on provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money invested provides the term of exchange between a given amount of money capital.
- For provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money given provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate, provides the term of exchange between a given amount of money Higher provides the term of exchange between a given amount of money compounding provides the term of exchange between a given amount of money frequency provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money higher provides the term of exchange between a given amount of money pay provides the term of exchange between a given amount of money off
- For provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money given provides the term of exchange between a given amount of money payoff, provides the term of exchange between a given amount of money higher provides the term of exchange between a given amount of money compounding provides the term of exchange between a given amount of money frequency provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money lower provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate
There provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money annual, provides the term of exchange between a given amount of money semi-annual, provides the term of exchange between a given amount of money quarterly provides the term of exchange between a given amount of money compounding provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates. provides the term of exchange between a given amount of money If provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money compounded
interest provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money known provides the term of exchange between a given amount of money than provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money calculated provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money following provides the term of exchange between a given amount of money formula:
1
Z ( t ,T )=
1+ ( r n ( t , T ) n∗(T −t)
n )
If provides the term of exchange between a given amount of money you provides the term of exchange between a given amount of money do provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money know provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money but provides the term of exchange between a given amount of money just provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factor, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money formula provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money
rearranged provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money calculate provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate:
( )
1
r n ( t , T )=n∗ 1
−1
Z ( t ,T ) n∗(T −t)
When provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money compounding provides the term of exchange between a given amount of money frequency provides the term of exchange between a given amount of money n provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money increased provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money infinity provides the term of exchange between a given amount of money we provides the term of exchange between a given amount of money call provides the term of exchange between a given amount of money this provides the term of exchange between a given amount of money continuously
compounded interest rate. provides the term of exchange between a given amount of money Also, provides the term of exchange between a given amount of money for provides the term of exchange between a given amount of money these provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factor provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money
can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money calculated provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money two provides the term of exchange between a given amount of money formulas:
,Z ( t ,T )=e−r (t , T)(T−t )
−ln ( Z ( t , T ) )
r ( t , T )=
(T −t )
The provides the term of exchange between a given amount of money term structure of interest rates, provides the term of exchange between a given amount of money or spot curve, or yield curve, provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money certain provides the term of exchange between a given amount of money time provides the term of exchange between a given amount of money t provides the term of exchange between a given amount of money defines provides the term of exchange between a given amount of money
the provides the term of exchange between a given amount of money relation provides the term of exchange between a given amount of money between provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money level provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money their provides the term of exchange between a given amount of money time provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money T-t. provides the term of exchange between a given amount of money
The provides the term of exchange between a given amount of money term spread provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money difference provides the term of exchange between a given amount of money between provides the term of exchange between a given amount of money long provides the term of exchange between a given amount of money term provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money (e.g. provides the term of exchange between a given amount of money 10 provides the term of exchange between a given amount of money year provides the term of exchange between a given amount of money rate) provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money
the provides the term of exchange between a given amount of money short provides the term of exchange between a given amount of money term provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money (e.g. provides the term of exchange between a given amount of money 3 provides the term of exchange between a given amount of money month provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate). provides the term of exchange between a given amount of money The provides the term of exchange between a given amount of money term provides the term of exchange between a given amount of money spread provides the term of exchange between a given amount of money depends provides the term of exchange between a given amount of money on provides the term of exchange between a given amount of money many provides the term of exchange between a given amount of money
variables: provides the term of exchange between a given amount of money expected provides the term of exchange between a given amount of money future provides the term of exchange between a given amount of money inflation, provides the term of exchange between a given amount of money expected provides the term of exchange between a given amount of money growth provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money economy, provides the term of exchange between a given amount of money agents provides the term of exchange between a given amount of money attitude provides the term of exchange between a given amount of money
towards provides the term of exchange between a given amount of money risk, provides the term of exchange between a given amount of money etc.
Arbitrage opportunity
An provides the term of exchange between a given amount of money arbitrage provides the term of exchange between a given amount of money opportunity provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money feasible provides the term of exchange between a given amount of money trading provides the term of exchange between a given amount of money strategy provides the term of exchange between a given amount of money involving provides the term of exchange between a given amount of money two provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money more provides the term of exchange between a given amount of money securities provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money
either:
- No provides the term of exchange between a given amount of money cost provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money initiation, provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money generating provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money sure provides the term of exchange between a given amount of money positive provides the term of exchange between a given amount of money profit provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money certain provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money in provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money
future
- Generates provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money positive provides the term of exchange between a given amount of money payoff provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money initiation, provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money it provides the term of exchange between a given amount of money has provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money sure provides the term of exchange between a given amount of money non-negative provides the term of exchange between a given amount of money payoff provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money
certain provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money in provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money future
Law of one price provides the term of exchange between a given amount of money implies provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money assets provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money same provides the term of exchange between a given amount of money payoff provides the term of exchange between a given amount of money have provides the term of exchange between a given amount of money same provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money so provides the term of exchange between a given amount of money no provides the term of exchange between a given amount of money arbitrage
Zero coupon bonds
The provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money zero provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money (with provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money principal provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money $100) provides the term of exchange between a given amount of money are provides the term of exchange between a given amount of money equal provides the term of exchange between a given amount of money to:
P z ( t ,T )=100∗Z( t , T )
This provides the term of exchange between a given amount of money means provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money from provides the term of exchange between a given amount of money observed provides the term of exchange between a given amount of money prices provides the term of exchange between a given amount of money for provides the term of exchange between a given amount of money zero provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money we provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money compute provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money
factors.
Coupon bonds
Consider provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money time provides the term of exchange between a given amount of money t provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money c, provides the term of exchange between a given amount of money semi-annual provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money payment provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money
payment provides the term of exchange between a given amount of money dates. provides the term of exchange between a given amount of money There provides the term of exchange between a given amount of money will provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money for provides the term of exchange between a given amount of money each provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money T. provides the term of exchange between a given amount of money The provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money
can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money computed provides the term of exchange between a given amount of money as:
n
c∗100
Pc ( t , T n ) = ∗∑ Z ( t , T i ) +100∗Z(t , T n )
2 i=1
Z ( t ,T n ) → discount factor ∈the year of maturity of the coupon bond provides the term of exchange between a given amount of money
Also:
n
c
Pc ( t , T n ) = ∗∑ Pz ( t ,T i ) +100∗P z ( t ,T n )
2 i=1
Bootstrap methodology provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money enough provides the term of exchange between a given amount of money data, provides the term of exchange between a given amount of money you provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money compute provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money zero- provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money
bond provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money prices provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond. provides the term of exchange between a given amount of money You provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money obtain provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money each provides the term of exchange between a given amount of money maturity.
Pc (t , T 1 )
Z ( t ,T 1 )=
c provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money Z ( t ,T i )=P c ( t , T i )−100∗¿ ¿
100∗(1+ 1 )
2
, In provides the term of exchange between a given amount of money practice provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money bootstrap provides the term of exchange between a given amount of money method provides the term of exchange between a given amount of money might provides the term of exchange between a given amount of money break provides the term of exchange between a given amount of money down, provides the term of exchange between a given amount of money in provides the term of exchange between a given amount of money particular provides the term of exchange between a given amount of money because provides the term of exchange between a given amount of money liquid provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money
might provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money available provides the term of exchange between a given amount of money for provides the term of exchange between a given amount of money all provides the term of exchange between a given amount of money (longer) provides the term of exchange between a given amount of money maturities.
Nelson-Siegel method
−T ,t
( θ1 +θ2 )∗1−e λ
r ( t , T )=θ0 + −θ 2 e−(T ,t )/ λ provides the term of exchange between a given amount of money
T ,T
λ
θ0 → controlsthe level of the term strucutre
θ1 → determines the slope
θ2∧ λ → determinethe shape of the term structure
Yield to maturity
The provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money (YTM) provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money defined provides the term of exchange between a given amount of money as provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money makes provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money
present provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money cash provides the term of exchange between a given amount of money flows provides the term of exchange between a given amount of money (coupons provides the term of exchange between a given amount of money + provides the term of exchange between a given amount of money principal) provides the term of exchange between a given amount of money equal provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money bond. provides the term of exchange between a given amount of money Similar provides the term of exchange between a given amount of money
to provides the term of exchange between a given amount of money an provides the term of exchange between a given amount of money internal provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money return provides the term of exchange between a given amount of money (IRR). provides the term of exchange between a given amount of money For provides the term of exchange between a given amount of money example, provides the term of exchange between a given amount of money semi-annual:
c
n ∗100
2 100
Pc ( t , T n ) =∑ +
( ) ( )
2∗(T ,t )
i=1 y i
y 2∗(T −t ) n
1+ 1+
2 2
Yield provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money kind provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money weighted provides the term of exchange between a given amount of money average provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money spot provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money corresponding provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money
different provides the term of exchange between a given amount of money cash provides the term of exchange between a given amount of money flows provides the term of exchange between a given amount of money paid provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money bond. provides the term of exchange between a given amount of money The provides the term of exchange between a given amount of money higher provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money specific provides the term of exchange between a given amount of money cash provides the term of exchange between a given amount of money flow, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money higher provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money weight provides the term of exchange between a given amount of money on provides the term of exchange between a given amount of money
that provides the term of exchange between a given amount of money spot provides the term of exchange between a given amount of money rate. provides the term of exchange between a given amount of money YTM provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money convenient provides the term of exchange between a given amount of money summary provides the term of exchange between a given amount of money measure, provides the term of exchange between a given amount of money but provides the term of exchange between a given amount of money it provides the term of exchange between a given amount of money has provides the term of exchange between a given amount of money limitations:
- You provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money only provides the term of exchange between a given amount of money calculate provides the term of exchange between a given amount of money it provides the term of exchange between a given amount of money after provides the term of exchange between a given amount of money you provides the term of exchange between a given amount of money know provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money bond’s provides the term of exchange between a given amount of money price.
- It provides the term of exchange between a given amount of money only provides the term of exchange between a given amount of money applies provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money single provides the term of exchange between a given amount of money bond
IMPORTANT: provides the term of exchange between a given amount of money Yield provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money often provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money good provides the term of exchange between a given amount of money way provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money compare provides the term of exchange between a given amount of money investment provides the term of exchange between a given amount of money decisions. provides the term of exchange between a given amount of money
- If provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money curve provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money flat, provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money different provides the term of exchange between a given amount of money maturities provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money will provides the term of exchange between a given amount of money
almost provides the term of exchange between a given amount of money always provides the term of exchange between a given amount of money have provides the term of exchange between a given amount of money different provides the term of exchange between a given amount of money yields provides the term of exchange between a given amount of money
- The provides the term of exchange between a given amount of money YTMs provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money two provides the term of exchange between a given amount of money fairly provides the term of exchange between a given amount of money priced provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money will provides the term of exchange between a given amount of money differ provides the term of exchange between a given amount of money if provides the term of exchange between a given amount of money they provides the term of exchange between a given amount of money have provides the term of exchange between a given amount of money different provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money
maturities provides the term of exchange between a given amount of money
Floating rate bonds
The provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money floating provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money without provides the term of exchange between a given amount of money spread provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money equal provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money their provides the term of exchange between a given amount of money face provides the term of exchange between a given amount of money value. provides the term of exchange between a given amount of money
Each provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money also provides the term of exchange between a given amount of money called provides the term of exchange between a given amount of money reset date provides the term of exchange between a given amount of money as provides the term of exchange between a given amount of money it provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money time provides the term of exchange between a given amount of money when provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money new provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money reset. provides the term of exchange between a given amount of money So provides the term of exchange between a given amount of money
always provides the term of exchange between a given amount of money after provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money reset provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money face provides the term of exchange between a given amount of money value.
n
100∗s
Price with spread= price of no spread bond+ ∗∑ Z (0 ,t )
2 t=i
Price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money no provides the term of exchange between a given amount of money spread provides the term of exchange between a given amount of money bond:
P FR ( t ,T )=Z ( t , T i+ 1)∗100∗¿
The expectations hypothesis
Under provides the term of exchange between a given amount of money perfect provides the term of exchange between a given amount of money foresight, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money long-term provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money weighted provides the term of exchange between a given amount of money average provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money current provides the term of exchange between a given amount of money short-term provides the term of exchange between a given amount of money
yield provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money short-term provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money next provides the term of exchange between a given amount of money period
- If provides the term of exchange between a given amount of money market provides the term of exchange between a given amount of money participants provides the term of exchange between a given amount of money expect provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money increase, provides the term of exchange between a given amount of money then provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money curve provides the term of exchange between a given amount of money slopes provides the term of exchange between a given amount of money
upwards
Discount factor Z(t,T) provides the term of exchange between a given amount of money provides provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money term provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money exchange provides the term of exchange between a given amount of money between provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money given provides the term of exchange between a given amount of money amount provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money money provides the term of exchange between a given amount of money
at provides the term of exchange between a given amount of money t provides the term of exchange between a given amount of money versus provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money (certain) provides the term of exchange between a given amount of money amount provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money money provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money later provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money T.
Z(t,T) provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money seen provides the term of exchange between a given amount of money as provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money zero provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money $1 provides the term of exchange between a given amount of money face provides the term of exchange between a given amount of money value, provides the term of exchange between a given amount of money maturing provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money T. provides the term of exchange between a given amount of money It provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money
usually provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money case provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money market provides the term of exchange between a given amount of money participants provides the term of exchange between a given amount of money prefer provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money $1 provides the term of exchange between a given amount of money sooner provides the term of exchange between a given amount of money than provides the term of exchange between a given amount of money later, provides the term of exchange between a given amount of money hence provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money any provides the term of exchange between a given amount of money given provides the term of exchange between a given amount of money
time provides the term of exchange between a given amount of money t, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factor provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money usually provides the term of exchange between a given amount of money lower, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money longer provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money T.
Discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money are provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money constant provides the term of exchange between a given amount of money over provides the term of exchange between a given amount of money time, provides the term of exchange between a given amount of money one provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money variables provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money determines provides the term of exchange between a given amount of money this provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money
is provides the term of exchange between a given amount of money inflation:
- Higher provides the term of exchange between a given amount of money expected provides the term of exchange between a given amount of money inflation provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money money provides the term of exchange between a given amount of money less provides the term of exchange between a given amount of money valuable provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money go provides the term of exchange between a given amount of money down
Other provides the term of exchange between a given amount of money variables provides the term of exchange between a given amount of money are:
- Real provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money fluctuate
- There provides the term of exchange between a given amount of money may provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money temporary provides the term of exchange between a given amount of money liquidity provides the term of exchange between a given amount of money effects
The compounding frequency of interest accruals provides the term of exchange between a given amount of money refers provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money number provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money times provides the term of exchange between a given amount of money within provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money year
in provides the term of exchange between a given amount of money which provides the term of exchange between a given amount of money interests provides the term of exchange between a given amount of money are provides the term of exchange between a given amount of money paid provides the term of exchange between a given amount of money on provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money invested provides the term of exchange between a given amount of money capital.
- For provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money given provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate, provides the term of exchange between a given amount of money Higher provides the term of exchange between a given amount of money compounding provides the term of exchange between a given amount of money frequency provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money higher provides the term of exchange between a given amount of money pay provides the term of exchange between a given amount of money off
- For provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money given provides the term of exchange between a given amount of money payoff, provides the term of exchange between a given amount of money higher provides the term of exchange between a given amount of money compounding provides the term of exchange between a given amount of money frequency provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money lower provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate
There provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money annual, provides the term of exchange between a given amount of money semi-annual, provides the term of exchange between a given amount of money quarterly provides the term of exchange between a given amount of money compounding provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates. provides the term of exchange between a given amount of money If provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money compounded
interest provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money known provides the term of exchange between a given amount of money than provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money calculated provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money following provides the term of exchange between a given amount of money formula:
1
Z ( t ,T )=
1+ ( r n ( t , T ) n∗(T −t)
n )
If provides the term of exchange between a given amount of money you provides the term of exchange between a given amount of money do provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money know provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money but provides the term of exchange between a given amount of money just provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factor, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money formula provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money
rearranged provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money calculate provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate:
( )
1
r n ( t , T )=n∗ 1
−1
Z ( t ,T ) n∗(T −t)
When provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money compounding provides the term of exchange between a given amount of money frequency provides the term of exchange between a given amount of money n provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money increased provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money infinity provides the term of exchange between a given amount of money we provides the term of exchange between a given amount of money call provides the term of exchange between a given amount of money this provides the term of exchange between a given amount of money continuously
compounded interest rate. provides the term of exchange between a given amount of money Also, provides the term of exchange between a given amount of money for provides the term of exchange between a given amount of money these provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factor provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money
can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money calculated provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money two provides the term of exchange between a given amount of money formulas:
,Z ( t ,T )=e−r (t , T)(T−t )
−ln ( Z ( t , T ) )
r ( t , T )=
(T −t )
The provides the term of exchange between a given amount of money term structure of interest rates, provides the term of exchange between a given amount of money or spot curve, or yield curve, provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money certain provides the term of exchange between a given amount of money time provides the term of exchange between a given amount of money t provides the term of exchange between a given amount of money defines provides the term of exchange between a given amount of money
the provides the term of exchange between a given amount of money relation provides the term of exchange between a given amount of money between provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money level provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money their provides the term of exchange between a given amount of money time provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money T-t. provides the term of exchange between a given amount of money
The provides the term of exchange between a given amount of money term spread provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money difference provides the term of exchange between a given amount of money between provides the term of exchange between a given amount of money long provides the term of exchange between a given amount of money term provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money (e.g. provides the term of exchange between a given amount of money 10 provides the term of exchange between a given amount of money year provides the term of exchange between a given amount of money rate) provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money
the provides the term of exchange between a given amount of money short provides the term of exchange between a given amount of money term provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money (e.g. provides the term of exchange between a given amount of money 3 provides the term of exchange between a given amount of money month provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rate). provides the term of exchange between a given amount of money The provides the term of exchange between a given amount of money term provides the term of exchange between a given amount of money spread provides the term of exchange between a given amount of money depends provides the term of exchange between a given amount of money on provides the term of exchange between a given amount of money many provides the term of exchange between a given amount of money
variables: provides the term of exchange between a given amount of money expected provides the term of exchange between a given amount of money future provides the term of exchange between a given amount of money inflation, provides the term of exchange between a given amount of money expected provides the term of exchange between a given amount of money growth provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money economy, provides the term of exchange between a given amount of money agents provides the term of exchange between a given amount of money attitude provides the term of exchange between a given amount of money
towards provides the term of exchange between a given amount of money risk, provides the term of exchange between a given amount of money etc.
Arbitrage opportunity
An provides the term of exchange between a given amount of money arbitrage provides the term of exchange between a given amount of money opportunity provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money feasible provides the term of exchange between a given amount of money trading provides the term of exchange between a given amount of money strategy provides the term of exchange between a given amount of money involving provides the term of exchange between a given amount of money two provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money more provides the term of exchange between a given amount of money securities provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money
either:
- No provides the term of exchange between a given amount of money cost provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money initiation, provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money generating provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money sure provides the term of exchange between a given amount of money positive provides the term of exchange between a given amount of money profit provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money certain provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money in provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money
future
- Generates provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money positive provides the term of exchange between a given amount of money payoff provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money initiation, provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money it provides the term of exchange between a given amount of money has provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money sure provides the term of exchange between a given amount of money non-negative provides the term of exchange between a given amount of money payoff provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money
certain provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money in provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money future
Law of one price provides the term of exchange between a given amount of money implies provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money assets provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money same provides the term of exchange between a given amount of money payoff provides the term of exchange between a given amount of money have provides the term of exchange between a given amount of money same provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money so provides the term of exchange between a given amount of money no provides the term of exchange between a given amount of money arbitrage
Zero coupon bonds
The provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money zero provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money (with provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money principal provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money $100) provides the term of exchange between a given amount of money are provides the term of exchange between a given amount of money equal provides the term of exchange between a given amount of money to:
P z ( t ,T )=100∗Z( t , T )
This provides the term of exchange between a given amount of money means provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money from provides the term of exchange between a given amount of money observed provides the term of exchange between a given amount of money prices provides the term of exchange between a given amount of money for provides the term of exchange between a given amount of money zero provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money we provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money compute provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money
factors.
Coupon bonds
Consider provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money at provides the term of exchange between a given amount of money time provides the term of exchange between a given amount of money t provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money c, provides the term of exchange between a given amount of money semi-annual provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money payment provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money
payment provides the term of exchange between a given amount of money dates. provides the term of exchange between a given amount of money There provides the term of exchange between a given amount of money will provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money for provides the term of exchange between a given amount of money each provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money T. provides the term of exchange between a given amount of money The provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money
can provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money computed provides the term of exchange between a given amount of money as:
n
c∗100
Pc ( t , T n ) = ∗∑ Z ( t , T i ) +100∗Z(t , T n )
2 i=1
Z ( t ,T n ) → discount factor ∈the year of maturity of the coupon bond provides the term of exchange between a given amount of money
Also:
n
c
Pc ( t , T n ) = ∗∑ Pz ( t ,T i ) +100∗P z ( t ,T n )
2 i=1
Bootstrap methodology provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money enough provides the term of exchange between a given amount of money data, provides the term of exchange between a given amount of money you provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money compute provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money zero- provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money
bond provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money prices provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond. provides the term of exchange between a given amount of money You provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money obtain provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money factors provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money each provides the term of exchange between a given amount of money maturity.
Pc (t , T 1 )
Z ( t ,T 1 )=
c provides the term of exchange between a given amount of money provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money Z ( t ,T i )=P c ( t , T i )−100∗¿ ¿
100∗(1+ 1 )
2
, In provides the term of exchange between a given amount of money practice provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money bootstrap provides the term of exchange between a given amount of money method provides the term of exchange between a given amount of money might provides the term of exchange between a given amount of money break provides the term of exchange between a given amount of money down, provides the term of exchange between a given amount of money in provides the term of exchange between a given amount of money particular provides the term of exchange between a given amount of money because provides the term of exchange between a given amount of money liquid provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money
might provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money be provides the term of exchange between a given amount of money available provides the term of exchange between a given amount of money for provides the term of exchange between a given amount of money all provides the term of exchange between a given amount of money (longer) provides the term of exchange between a given amount of money maturities.
Nelson-Siegel method
−T ,t
( θ1 +θ2 )∗1−e λ
r ( t , T )=θ0 + −θ 2 e−(T ,t )/ λ provides the term of exchange between a given amount of money
T ,T
λ
θ0 → controlsthe level of the term strucutre
θ1 → determines the slope
θ2∧ λ → determinethe shape of the term structure
Yield to maturity
The provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money (YTM) provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money defined provides the term of exchange between a given amount of money as provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money discount provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money that provides the term of exchange between a given amount of money makes provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money
present provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money cash provides the term of exchange between a given amount of money flows provides the term of exchange between a given amount of money (coupons provides the term of exchange between a given amount of money + provides the term of exchange between a given amount of money principal) provides the term of exchange between a given amount of money equal provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money bond. provides the term of exchange between a given amount of money Similar provides the term of exchange between a given amount of money
to provides the term of exchange between a given amount of money an provides the term of exchange between a given amount of money internal provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money return provides the term of exchange between a given amount of money (IRR). provides the term of exchange between a given amount of money For provides the term of exchange between a given amount of money example, provides the term of exchange between a given amount of money semi-annual:
c
n ∗100
2 100
Pc ( t , T n ) =∑ +
( ) ( )
2∗(T ,t )
i=1 y i
y 2∗(T −t ) n
1+ 1+
2 2
Yield provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money kind provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money weighted provides the term of exchange between a given amount of money average provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money spot provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money corresponding provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money
different provides the term of exchange between a given amount of money cash provides the term of exchange between a given amount of money flows provides the term of exchange between a given amount of money paid provides the term of exchange between a given amount of money by provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money bond. provides the term of exchange between a given amount of money The provides the term of exchange between a given amount of money higher provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money specific provides the term of exchange between a given amount of money cash provides the term of exchange between a given amount of money flow, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money higher provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money weight provides the term of exchange between a given amount of money on provides the term of exchange between a given amount of money
that provides the term of exchange between a given amount of money spot provides the term of exchange between a given amount of money rate. provides the term of exchange between a given amount of money YTM provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money convenient provides the term of exchange between a given amount of money summary provides the term of exchange between a given amount of money measure, provides the term of exchange between a given amount of money but provides the term of exchange between a given amount of money it provides the term of exchange between a given amount of money has provides the term of exchange between a given amount of money limitations:
- You provides the term of exchange between a given amount of money can provides the term of exchange between a given amount of money only provides the term of exchange between a given amount of money calculate provides the term of exchange between a given amount of money it provides the term of exchange between a given amount of money after provides the term of exchange between a given amount of money you provides the term of exchange between a given amount of money know provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money bond’s provides the term of exchange between a given amount of money price.
- It provides the term of exchange between a given amount of money only provides the term of exchange between a given amount of money applies provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money single provides the term of exchange between a given amount of money bond
IMPORTANT: provides the term of exchange between a given amount of money Yield provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money maturity provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money often provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money good provides the term of exchange between a given amount of money way provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money compare provides the term of exchange between a given amount of money investment provides the term of exchange between a given amount of money decisions. provides the term of exchange between a given amount of money
- If provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money curve provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money not provides the term of exchange between a given amount of money flat, provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money with provides the term of exchange between a given amount of money different provides the term of exchange between a given amount of money maturities provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money will provides the term of exchange between a given amount of money
almost provides the term of exchange between a given amount of money always provides the term of exchange between a given amount of money have provides the term of exchange between a given amount of money different provides the term of exchange between a given amount of money yields provides the term of exchange between a given amount of money
- The provides the term of exchange between a given amount of money YTMs provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money two provides the term of exchange between a given amount of money fairly provides the term of exchange between a given amount of money priced provides the term of exchange between a given amount of money bonds provides the term of exchange between a given amount of money will provides the term of exchange between a given amount of money differ provides the term of exchange between a given amount of money if provides the term of exchange between a given amount of money they provides the term of exchange between a given amount of money have provides the term of exchange between a given amount of money different provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money or provides the term of exchange between a given amount of money
maturities provides the term of exchange between a given amount of money
Floating rate bonds
The provides the term of exchange between a given amount of money price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money floating provides the term of exchange between a given amount of money rate provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money without provides the term of exchange between a given amount of money spread provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money equal provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money their provides the term of exchange between a given amount of money face provides the term of exchange between a given amount of money value. provides the term of exchange between a given amount of money
Each provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money also provides the term of exchange between a given amount of money called provides the term of exchange between a given amount of money reset date provides the term of exchange between a given amount of money as provides the term of exchange between a given amount of money it provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money time provides the term of exchange between a given amount of money when provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money new provides the term of exchange between a given amount of money coupon provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money reset. provides the term of exchange between a given amount of money So provides the term of exchange between a given amount of money
always provides the term of exchange between a given amount of money after provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money reset provides the term of exchange between a given amount of money date provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money value provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money bond provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money face provides the term of exchange between a given amount of money value.
n
100∗s
Price with spread= price of no spread bond+ ∗∑ Z (0 ,t )
2 t=i
Price provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money no provides the term of exchange between a given amount of money spread provides the term of exchange between a given amount of money bond:
P FR ( t ,T )=Z ( t , T i+ 1)∗100∗¿
The expectations hypothesis
Under provides the term of exchange between a given amount of money perfect provides the term of exchange between a given amount of money foresight, provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money long-term provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money is provides the term of exchange between a given amount of money a provides the term of exchange between a given amount of money weighted provides the term of exchange between a given amount of money average provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money current provides the term of exchange between a given amount of money short-term provides the term of exchange between a given amount of money
yield provides the term of exchange between a given amount of money and provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money short-term provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money of provides the term of exchange between a given amount of money next provides the term of exchange between a given amount of money period
- If provides the term of exchange between a given amount of money market provides the term of exchange between a given amount of money participants provides the term of exchange between a given amount of money expect provides the term of exchange between a given amount of money interest provides the term of exchange between a given amount of money rates provides the term of exchange between a given amount of money to provides the term of exchange between a given amount of money increase, provides the term of exchange between a given amount of money then provides the term of exchange between a given amount of money the provides the term of exchange between a given amount of money yield provides the term of exchange between a given amount of money curve provides the term of exchange between a given amount of money slopes provides the term of exchange between a given amount of money
upwards
