, List of Symbols
α ¼ alpha, unsystematic return
A0, AT ¼ market value of firm assets at time 0 and T
AI, AIt, AIT ¼ accrued interest today, at time t, and at time T
b, bt, bT ¼ basis today, at time t, and at expiration, T
B ¼ market value of bond portfolio
β, βs, βf, βT, βy ¼ beta, beta of spot asset or portfolio, beta of futures, target
beta, and yield beta
B0, BT ¼ market value of firm debt at time 0 and T
B0(ti) ¼ price of zero coupon bond observed at time 0, matures in
ti days
C ¼ (abbreviated) price of call
C1, C2, C3 ¼ (abbreviated) price of call for exercise prices X1, X2, X3
C(S0,T,X) ¼ price of either European or American call on asset with
price S0, expiration T, and exercise price X
Ce(S0,T,X) ¼ price of European call on asset with price S0, expiration T,
and exercise price X
Ca(S0,T,X) ¼ price of American call on asset with price S0, expiration T,
and exercise price X
C(f0,T,X) ¼ price of either European or American call on futures with
price f0, expiration T, and exercise price X
Ce(f0,T,X) ¼ price of European call on futures with price f0, expiration T,
and exercise price X
Ca(f0,T,X) ¼ price of American call on futures with price f0, expiration T,
and exercise price X
Cu, Cd, Cu2, Cud, Cd2 ¼ call price sequence in binomial model
χ ¼ convenience yield
CIt ¼ coupon interest paid at time t
CovΔS,Δf ¼ covariance of the change in the spot price and change in
the futures price
CovrS ,rf ¼ covariance of the rate of return on the spot and futures
ρΔS,Δf ¼ correlation of the change in the spot price and change in
the futures price
CPt ¼ cash payment (principal or interest) on bond at time t
CF ¼ conversion factor on CBOT T-bond contract
CF(t), CF(T) ¼ conversion factor on CBOT T-bond contracts deliverable
at times t and T
c ¼ coupon rate
Δ ¼ delta of an option
ΔB, ΔM, ΔS, Δf, ΔyB, Δyf ¼ change in bond price, change in market portfolio value,
change in spot price, change in futures price, change in
bond yield, change in futures yield
δc ¼ dividend yield
d ¼ (without subscript) 1.0 + downward return on stock in
binomial model
d1 , d2 ¼ variables in Black-Scholes-Merton model
, D0, D ¼ present value of dividends to time 0, present value of dividends
Dj, Dt ¼ dividend paid at time j or time t
DT ¼ compound future value of reinvested dividends
DURB ¼ Macaulay’s duration
ε¼ standard normal random variable in Monte Carlo simulation
E(x) ¼ expected value of the argument x
e* ¼ measure of hedging effectiveness
f0, ft, fT, f¼ (abbreviated) futures price at time 0, t, and T, value of futures
position
f0(T), ft(T), fT(T) ¼ futures price or futures exchange rate today, at time t, and at
expiration T
f0(T)(a)‡ ¼ critical futures price for early exercise of American option on
futures
F ¼ fixed rate on FRAs or continuously compounded forward rate
F(0,T) ¼ forward price for contracts written today 0, expiring at T
FV ¼ face value of bond
g ¼ days elapsed in FRA
Γ ¼ gamma of an option
h ¼ number of days in FRA when originated
hC, hS ¼ hedge ratios based on Black-Scholes-Merton model
h, hu, hd ¼ hedge ratios in binomial model
i ¼ interest rate for storage problem
J ¼ number of observations in sample
j ¼ counter in summation procedure
K ¼ parameter in break forward contract
k ¼ discount rate (required rate) on stock
LIBOR ¼ London Interbank Offer Rate, a Eurodollar rate
ln(x) ¼ natural log of the argument x
Lt(h) ¼ h-day LIBOR at t
m ¼ number of days associated with interest rate
M ¼ value of market portfolio of all risky assets
MDB, MDf, MDT ¼ modified duration of bond portfolio, modified duration of futures
contract, target modified duration
MOS ¼ number of months in computing CBOT conversion factor
MOS* ¼ number of months in computing CBOT conversion factor
rounded down to nearest quarter
N ¼ total number in summation procedure
N1, N2, N3 ¼ quantity of options
N(d1), N(d2) ¼ cumulative normal probabilities in Black-Scholes-Merton model
Nf* ¼ optimal hedge ratio
NPV ¼ net present value
NB, NC, NP, NS, Nf ¼ number of bonds, calls, puts, shares of stock, and futures held
in a position
NP, NP€, NP$ ¼ notional principle, euros, dollars
, An Introduction to Derivatives
and Risk Management
EIGHTH EDITION
DON M. CHANCE
Louisiana State University
ROBERT BROOKS
University of Alabama
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
α ¼ alpha, unsystematic return
A0, AT ¼ market value of firm assets at time 0 and T
AI, AIt, AIT ¼ accrued interest today, at time t, and at time T
b, bt, bT ¼ basis today, at time t, and at expiration, T
B ¼ market value of bond portfolio
β, βs, βf, βT, βy ¼ beta, beta of spot asset or portfolio, beta of futures, target
beta, and yield beta
B0, BT ¼ market value of firm debt at time 0 and T
B0(ti) ¼ price of zero coupon bond observed at time 0, matures in
ti days
C ¼ (abbreviated) price of call
C1, C2, C3 ¼ (abbreviated) price of call for exercise prices X1, X2, X3
C(S0,T,X) ¼ price of either European or American call on asset with
price S0, expiration T, and exercise price X
Ce(S0,T,X) ¼ price of European call on asset with price S0, expiration T,
and exercise price X
Ca(S0,T,X) ¼ price of American call on asset with price S0, expiration T,
and exercise price X
C(f0,T,X) ¼ price of either European or American call on futures with
price f0, expiration T, and exercise price X
Ce(f0,T,X) ¼ price of European call on futures with price f0, expiration T,
and exercise price X
Ca(f0,T,X) ¼ price of American call on futures with price f0, expiration T,
and exercise price X
Cu, Cd, Cu2, Cud, Cd2 ¼ call price sequence in binomial model
χ ¼ convenience yield
CIt ¼ coupon interest paid at time t
CovΔS,Δf ¼ covariance of the change in the spot price and change in
the futures price
CovrS ,rf ¼ covariance of the rate of return on the spot and futures
ρΔS,Δf ¼ correlation of the change in the spot price and change in
the futures price
CPt ¼ cash payment (principal or interest) on bond at time t
CF ¼ conversion factor on CBOT T-bond contract
CF(t), CF(T) ¼ conversion factor on CBOT T-bond contracts deliverable
at times t and T
c ¼ coupon rate
Δ ¼ delta of an option
ΔB, ΔM, ΔS, Δf, ΔyB, Δyf ¼ change in bond price, change in market portfolio value,
change in spot price, change in futures price, change in
bond yield, change in futures yield
δc ¼ dividend yield
d ¼ (without subscript) 1.0 + downward return on stock in
binomial model
d1 , d2 ¼ variables in Black-Scholes-Merton model
, D0, D ¼ present value of dividends to time 0, present value of dividends
Dj, Dt ¼ dividend paid at time j or time t
DT ¼ compound future value of reinvested dividends
DURB ¼ Macaulay’s duration
ε¼ standard normal random variable in Monte Carlo simulation
E(x) ¼ expected value of the argument x
e* ¼ measure of hedging effectiveness
f0, ft, fT, f¼ (abbreviated) futures price at time 0, t, and T, value of futures
position
f0(T), ft(T), fT(T) ¼ futures price or futures exchange rate today, at time t, and at
expiration T
f0(T)(a)‡ ¼ critical futures price for early exercise of American option on
futures
F ¼ fixed rate on FRAs or continuously compounded forward rate
F(0,T) ¼ forward price for contracts written today 0, expiring at T
FV ¼ face value of bond
g ¼ days elapsed in FRA
Γ ¼ gamma of an option
h ¼ number of days in FRA when originated
hC, hS ¼ hedge ratios based on Black-Scholes-Merton model
h, hu, hd ¼ hedge ratios in binomial model
i ¼ interest rate for storage problem
J ¼ number of observations in sample
j ¼ counter in summation procedure
K ¼ parameter in break forward contract
k ¼ discount rate (required rate) on stock
LIBOR ¼ London Interbank Offer Rate, a Eurodollar rate
ln(x) ¼ natural log of the argument x
Lt(h) ¼ h-day LIBOR at t
m ¼ number of days associated with interest rate
M ¼ value of market portfolio of all risky assets
MDB, MDf, MDT ¼ modified duration of bond portfolio, modified duration of futures
contract, target modified duration
MOS ¼ number of months in computing CBOT conversion factor
MOS* ¼ number of months in computing CBOT conversion factor
rounded down to nearest quarter
N ¼ total number in summation procedure
N1, N2, N3 ¼ quantity of options
N(d1), N(d2) ¼ cumulative normal probabilities in Black-Scholes-Merton model
Nf* ¼ optimal hedge ratio
NPV ¼ net present value
NB, NC, NP, NS, Nf ¼ number of bonds, calls, puts, shares of stock, and futures held
in a position
NP, NP€, NP$ ¼ notional principle, euros, dollars
, An Introduction to Derivatives
and Risk Management
EIGHTH EDITION
DON M. CHANCE
Louisiana State University
ROBERT BROOKS
University of Alabama
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
