Lecture Week 1 – 08/02/2021
Spot Exchange Rate – price at which you exchange two currencies now.
Exchange rates are expressed as fractions: S0 = 0.9 $/€ à pay $1 for €0.9 or vice-versa
2 typical sources of confusion:
1. Are you buying or selling?
2. Real world uses different notation à not a fraction.
𝑞𝑢𝑜𝑡𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦
𝑏𝑎𝑠𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦
- Quote currency said to have direct quote
- Base currency said to have indirect quote
USD/EUR à not a fraction
- Means USD is base and EUR is quote
- In our case this means €/$
- We will not use the USD/EUR notation in this course as to avoid confusion
American and European Quotes:
- American terms à USD is quote currency
- European terms à USD is base currency
Cross-currency rate: synthetic exchange rate obtained by combining 2 quoted exchange rates.
X = $/€ x Y/$ = Y/€
Arbitrage: arbitrage activity keeps synthetic and quoted rates close.
Bid-Ask Spread: market makers revenue comes from the bid-ask spread.
- If you were to keep buying and selling the same currency you would make a loss à
market makers profit.
Bid: €1 buys me $1.213 Ask: Need to sell $1.214 for €1
Anti-confusion tips:
1. Dealer needs to make a profit à correct exchange rate to use is always the one least
convenient for you.
2. Bid quote is the smaller one.
,Bid-Ask spread and Cross-Currency rates:
- Ask yourself 2 things:
- 1. How many GBP can I buy using EUR (bid-rate)
- 2. How many EUR can I buy using GBP (ask-rate)
Forward Rate: set exchange rate at t1 for a txn occurring at t2
Ft1, t2 à t1 is when F is decided, t2 is when transaction takes place.
- Most actions occur at short maturities.
Long or short a forward:
- Long EUR forward à buy € at forward rate.
- Short EUR forward à sell € at forward rate.
Eurocurrencies: has nothing to do with €
- An example: sizable amount of USD accumulated outside of the US.
Eurocurrency market: money market for borrowing and lending currencies that are held in the
form of deposits in banks located outside the country where the currency is issued as legal
tender.
, Lecture Week 2 – 15/02/2021
International Parity Conditions
The law of one price: if 2 financial instruments pay the same cash flows:
1. In the same moments in time
2. In the same states of nature
à they must have the same price; otherwise there is arbitrage opportunity.
- We can use the no arbitrage opportunity condition to price financial instruments
and/or form expectations about price movements.
Stochastic arbitrage: (speculation) à still exposed to risk. No speculation condition may hold
only on average.
Covered interest rate parity: used to be the closest thing in finance to a law of nature.
𝐹 €/$ 1 + 𝑖€
=
𝑆 €/$ 1 + 𝑖$
- Can be used to compute the fair forward price à no arbitrage opportunity
€ 1 + 𝑖€
𝐹 7$ = . 𝑆 €/$
1 + 𝑖$
- At this forward price, you don’t pay for entering long or short.
- Covered interest rate parity should always hold as a result of arbitrage activity.
Example of arbitrage strategy:
- Invest €1 in Europe à 1 x (1 + 0.015) = €1.015
- Convert €1 to $ à 1 x (1/0.9) x (1 + 0.035) x 0.92 = €1.058
- à clearly the CIRP is not holding as the two approaches differ.
FX hedging synthetic rate = the 5.8% interest rate that we “created” à the resulting demand
of this interest rate results in the elimination of the arbitrage opportunity.
Some definitions:
# €%$ & '! €%$
- Forward premium: 𝐹𝑃 =
'! €%$
o FP > 0 = euro trades at forward premium over the dollar
o FP < 0 = euro trades at a forward discount over the dollar
- Covered interest rate parity is approximated as: i€ - i$
Spot Exchange Rate – price at which you exchange two currencies now.
Exchange rates are expressed as fractions: S0 = 0.9 $/€ à pay $1 for €0.9 or vice-versa
2 typical sources of confusion:
1. Are you buying or selling?
2. Real world uses different notation à not a fraction.
𝑞𝑢𝑜𝑡𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦
𝑏𝑎𝑠𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦
- Quote currency said to have direct quote
- Base currency said to have indirect quote
USD/EUR à not a fraction
- Means USD is base and EUR is quote
- In our case this means €/$
- We will not use the USD/EUR notation in this course as to avoid confusion
American and European Quotes:
- American terms à USD is quote currency
- European terms à USD is base currency
Cross-currency rate: synthetic exchange rate obtained by combining 2 quoted exchange rates.
X = $/€ x Y/$ = Y/€
Arbitrage: arbitrage activity keeps synthetic and quoted rates close.
Bid-Ask Spread: market makers revenue comes from the bid-ask spread.
- If you were to keep buying and selling the same currency you would make a loss à
market makers profit.
Bid: €1 buys me $1.213 Ask: Need to sell $1.214 for €1
Anti-confusion tips:
1. Dealer needs to make a profit à correct exchange rate to use is always the one least
convenient for you.
2. Bid quote is the smaller one.
,Bid-Ask spread and Cross-Currency rates:
- Ask yourself 2 things:
- 1. How many GBP can I buy using EUR (bid-rate)
- 2. How many EUR can I buy using GBP (ask-rate)
Forward Rate: set exchange rate at t1 for a txn occurring at t2
Ft1, t2 à t1 is when F is decided, t2 is when transaction takes place.
- Most actions occur at short maturities.
Long or short a forward:
- Long EUR forward à buy € at forward rate.
- Short EUR forward à sell € at forward rate.
Eurocurrencies: has nothing to do with €
- An example: sizable amount of USD accumulated outside of the US.
Eurocurrency market: money market for borrowing and lending currencies that are held in the
form of deposits in banks located outside the country where the currency is issued as legal
tender.
, Lecture Week 2 – 15/02/2021
International Parity Conditions
The law of one price: if 2 financial instruments pay the same cash flows:
1. In the same moments in time
2. In the same states of nature
à they must have the same price; otherwise there is arbitrage opportunity.
- We can use the no arbitrage opportunity condition to price financial instruments
and/or form expectations about price movements.
Stochastic arbitrage: (speculation) à still exposed to risk. No speculation condition may hold
only on average.
Covered interest rate parity: used to be the closest thing in finance to a law of nature.
𝐹 €/$ 1 + 𝑖€
=
𝑆 €/$ 1 + 𝑖$
- Can be used to compute the fair forward price à no arbitrage opportunity
€ 1 + 𝑖€
𝐹 7$ = . 𝑆 €/$
1 + 𝑖$
- At this forward price, you don’t pay for entering long or short.
- Covered interest rate parity should always hold as a result of arbitrage activity.
Example of arbitrage strategy:
- Invest €1 in Europe à 1 x (1 + 0.015) = €1.015
- Convert €1 to $ à 1 x (1/0.9) x (1 + 0.035) x 0.92 = €1.058
- à clearly the CIRP is not holding as the two approaches differ.
FX hedging synthetic rate = the 5.8% interest rate that we “created” à the resulting demand
of this interest rate results in the elimination of the arbitrage opportunity.
Some definitions:
# €%$ & '! €%$
- Forward premium: 𝐹𝑃 =
'! €%$
o FP > 0 = euro trades at forward premium over the dollar
o FP < 0 = euro trades at a forward discount over the dollar
- Covered interest rate parity is approximated as: i€ - i$
