Chp 1
Currency Exchange Rates
organization
 Foreign exchange quotations
 Arbitrage
 Forward quotes
Currency Abbreviations
 Abbreviations are used to refer to the various
currencies. These abbreviations could be
commonly used symbols or “official” three-letter
codes.
 Financial newspapers such as the Financial Times
generally use symbols, while traders use threeletter codes. Symbols include $ (U.S. dollar), ¥
( Japanese yen), € (euro), £ (British pound), A$
(Australian dollar), and Sfr (Swiss franc).
 Three-letter codes for the same currencies are
USD, JPY, EUR, GBP, AUD, and CHF.
 We will alternatively use in this book (as done in
the real world) the various currency
abbreviations that are commonly encountered.
For example, the Japanese yen can be referred to
as ¥, JPY, or yen.
Foreign exchange quotations
 A currency exchange rate is the rate used
to exchange two currencies. An exchange
rate states the price of one currency in
terms of units of another currency.
 Examples: $:€, €:$, ¥:$
 Note: the notation in this new edition of
the text has changed relative to previous
editions.（€/£---- the number of euros
per pound ）
Quote Convention used in this text
 All quotes in this text will be presented as
a:b = S
– where a is the quoted currency
– b is the currency in which the price is expressed
– S is the price of the quoted currency a in units of
currency b
– For example, $:¥ = 130 means the U.S. dollar is
quoted at 130 Japanese yen (¥) per dollar. Or the
U.S. dollar is priced at 130 yen.
 Basic principles
1. All currencies are quoted against the U.S.
dollar, although there are such regional
exceptions as the yen in Asia and the euro and
pound in Europe.
Basic exchange rate
Cross exchange rate
From the quotation of two
currencies against the U.S. dollar,
one can derive the cross-exchange
rate between the two currencies
– For example, bank A gives the following quotations
• €:$ = 1.3364
• $:¥ = 123.52
– Calculate the euro in yen (€:¥) rate:
• (€:$)  ($:¥) = 1.3364  123.52 = 165.07
• The resulting quotation is: €:¥ = 165.07. One
euro is worth 165.07 yen.
– For example, bank B gives the following quotations for
the Korean won and the Brazilian real:
• $: won = 928.350
• $: R$ = 1.9094
– Calculate the R$:won rate:
• ($:won) ÷ ($:R$) = 928.35/1.9094 = 486.20
• The resulting quotation is: R$:won = 486.20.
One Brazilian Real is worth 486.50 won.
Fill in the missing exchange rates in the
following table.
Euro
US dollar
Yen
British
pound
Euro
US dollar Yen
British
pound
1
1.3 euro
2 euro
0.013 euro
Euro
Yen
US
dollar
British
pound
Euro
1
2 euro
US dollar
$0.77
1.3 euro 0.013
euro
1
$0.01
Yen
Yen 100 1
Yen
76.92
£0.5
£0.65
£0.0065
British
pound
$1.54
Yen 153.85
1
Conclusions:
(a:b) ×(b:c) = a:c
(a:b) ÷(a:c) = c :b
2. The Forex convention specifies rates for all
currencies per dollar (as in $:¥) except for the
pound and the euro.
 More on quotation conventions
direct exchange rate
quotation are made in terms of the amount of local
or domestic currency(DC) required to purchase one
unit of foreign currency(FC).
e.g. 100 yen per dollar
（appreciation and depreciation）
indirect exchange rate
traders quote the amount of foreign currency
required to purchase one unit of home
currency.
All exchange rate with dollar are usually given as direct
rates, but there are two exception that give the
indirect rates, The British pound and The euros.
 On July 1, the British pound (£) is
quoted as £:$ = 1.80.
– Is this a direct or indirect quote from
the viewpoint of an American and a
British investor?
– A month later, the exchange rate moved
to £:$ = 1.90. Which currencies
appreciated or depreciated?
American terms
the dollar price of one unit of the second
currency is referred to as American terms, a
direct quote in terms of U.S..
European terms
The amount of second currency per U.S. dollar
is called European terms, an indirect quote
from the U.S. perspective.
 other conventions
quotation are given with 5 digits.
Forex quotes always include a BID PRICE and
an ASK PRICE/OFFER PRICE, and there is
no commission or fee added on a trade
 Bid-ask(offer) quotes and spread
The Forex market is organized like an international OverThe-Counter market.
It is the price at which the dealer is
Bid price
willing to buy the quoted currency in
exchange for the second currency
Ask price It is price at which the dealer is willing
to sell the base currency in exchange
for the second currency.
The difference between the bid and ask price is
called the spread.
Midpoint price: (bid+ask)/2
Quote in U.S.
Bid
Ask
Direct (€:$)
$0.9836
$0.9839
Indirect ($:€)
€1.0164
€1.0167
Two principles
– The a:b ask exchange rate is the reciprocal of
the b:a bid exchange rate.
– The a:b bid exchange rate is the reciprocal of
the b:a ask exchange rate.
Indirect quotation =
1
Direct quotation
spread
 A pip stands for “price interest point” and represents
the smallest price fluctuation in the currency price. It
is equivalent to the “tick” on stock markets.
 E.g. €:$ = 1.3015 – 1.3019. The spread equals 4 pips.
Bid-ask spread = ask price – bid price
ask price
Example
Suppose bid price for £ = $1.52,
ask price = $1.60.
Spread = (1.60 – 1.52) = .05 or 5%
1.60
The difference is the
spread (gain)
The following factors will affect spread
 Trade volume
 Market condition
Arbitrage
 Cross-rate calculations with Bid-Ask spreads
(FC2：FC1)ask=(DC：FC1)ask * (FC2：DC)ask
(FC2：FC1)bid=(DC：FC1)bid * (FC2：DC)bid
Direct ask (FC：DC) = 1 / Indirect bid (DC：FC)
Direct bid (FC：DC) = 1 / Indirect ask (DC：FC)
– Notation: DC=domestic currency, FC=foreign
currency
Two check to be made correctly
Look at the symbols
Make sure that you maximize the bid-ask
spread
 An arbitrage could be created if it were
profitable to buy from one bank and sell to
another bank.
 Arbitrage aligns exchange rate quotations
throughout the world
– For example, the $:€ rate must be the same, at
a given instant, in Frankfurt, Paris and New
York.
There are two types of arbitrage with exchange rate
Bilateral arbitrage
Triangular arbitrage
Bilateral arbitrage
The law of one price
Equivalent assets sell for the same price,
exchange rate quotes in two countries should be
same within a transaction cost band.
the bid-ask spread in one country should be aligned
with the bid-ask spread in the other. If not, a
bilateral arbitrage opportunity exists.
Suppose
London
￡1=US$ 1.4815 ~ 1.4825
NewYork
￡l =US$ 1.4845 ~ 1.4855
Arbitrage Example
 Consider the following three banks each providing
a $:¥ quote :
Bank A
Bank B
Bank C
122.25-35
122.40-45
122.25-45
Does an arbitrage opportunity exist?
One could buy dollars from Bank A for 122.35 yen
per dollar and simultaneously sell them to Bank B
for 122.40 yen per dollar. A small gain, but it is
riskless and does not require any invested capital.
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Triangular arbitrage
It occurs if the quoted exchange rate between the
two currencies is higher or lower than the crossrate implied by the exchange rate of the two
currencies against the third currency.
You observe these rates:
– Tokyo $：¥
120.00
– NYC $: SFr 1.6000
– Zurich SFr: ¥ 80.00
Triangular arbitrage involves 3 steps
 Pick the cross rate currency
 Determine whether the cross-rate bid-ask quotes are in
line with the direct quotes by determining whether it is
cheaper to buy foreign currency directly or indirectly
 If not, an arbitrage opportunities exists.
If transaction costs are ignored
Check whether (FC1:DC)*(DC:FC2) *(FC2:FC1) =1
Transaction costs
Check whether quoted and cross-rate bid-ask spreads
overlap for any currency out of our three currencies.
If you have rate 1 [bid1, ask1] and rate 2 [bid2, ask2]
such that ask2<bid1, buy at ask2 and sell at bid1.
Triangular Arbitrage Example
You observe these quotes below. Is any currency arbitrage possible?
Frankfurt
London
New York
bid
ask
bid
ask
bid
ask
EUR：USD
0.9836 0.9839 GBP：EUR 1.5373 1.5380 USD：GBP 0.6566 0.6571
USD：EUR
1.0164 1.0167 EUR：GBP 0.6502 0.6505 GBP：USD 1.5219 1.5231
QUOTED
CROSS-RATES
bid
ask
bid
ask
EUR：USD 0.9836
0.9839 0.9895 0.9908
GBP：EUR 1.5373
1.5380 1.5469 1.5485
USD：GBP 0.6566
0.6571 0.6609 0.6614
Calculate cross-rates and compare with the quoted rates
Forward quotes
 Spot exchange rates are quoted for delivery two
business days after the transaction is concluded
 Forward exchange rate foreign exchange
traders quote exchange rates for delivery
further than two days in the future.
in other words, contract a commitment is
irrevocable made on the transaction date, but
delivery take places later, on a date set in the
contract.
Forward exchange rates are often quoted as a premium
or discount
Forward premium
– Nominal value in the forward exchange market is
higher than in the spot exchange market
Forward discount
– Nominal value in the forward exchange market is
lower than in the spot exchange market
Given an exchange rate of y：x, the annualized
forward premium on y
 Forward rate - Spot rate  
12




Spot rate

  No.months forward 
You observe the following: Spot USD/EUR=1.4570-76,
and 6-months forward USD/EUR=1.4408-34. Is EUR
trading at a premium or discount relative to the USD?
Compute the annualized forward discount/premium.
Interest rate parity: The forward discount and
the interest rate differential
 Interest rate parity
it is a relationship linking spot exchange rate,
forward exchange rate and interest rate.
for two currencies, FC and DC, the IRP is that
the forward discount equals the discounted
interest rate differential between the two
currencies.
（FFC：DC - S ）/ S = (rDC - rFC)/(1+rFC)
Riskless Arbitrage: Covered Interest Parity
 Spot: $: € = 0.8000
 One year interest rate ($): 10%
 One year interest rate (€): 14%
Time 0
Borrow at 10%
Time 1
Buying a
forward
contract
Spot $: € ?
U.S.D
F $: € =0.8080
Euros
Lend at 14%
1+r$ = S /F (1+r€)
F / S = (1+r€) / (1+r $)
(F- S) / S = (r€ - r $) / (1+ r $)
 ra  rb 
 Forward rate  Spot rate 


  
Spot rate


 1  ra 
Spot exchange rate = S a: b
Forward Quotations with Bid-Ask Spreads
- Example
 On the Forex market, you notice the
following quotes:
 Spot: $:¥ = 105.00 – 105.50
One year interest rate ($): 3 ½ – 4%
One year interest rate (¥): ½ - 1%
What should be the quote for the one year
forward exchange rate $:¥?
 Solution:
FASK
FBID
 1.04 
 105.50 
  109.174
 1.005 
 1.035 
 105.00 
  107.6
 1.01 
 Thus, the forward quotation is
$:¥: 107.60 – 109.174
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