International Financial Management
Chapter 3 The foreign exchange market
Michael Connolly
School of Business Administration,
University of Miami
Michael Connolly © 2007
Chapter 3 1

The foreign exchange market
Nearly two trillion dollars a day of foreign exchange or forex trading daily makes the FX market one of the largest financial markets.
It is made up of:
Daily global foreign exchange turnover in millions of USD (April 2004)
Spots
Forwards
FX Swaps
Options
$621,073
$208,333
$943,869
$113,608
33%
11%
50%
6%
Total $1,886,883 100%
Source: Bank of International Settlements,
Triennial Survey of Foreign Exchange and
Derivatives Markets, April 2004.
Chapter 3 Page 2



The foreign exchange market
The spot market in foreign exchange is for
“immediate delivery” on the spot or within two business days.
Forward and future markets for future delivery at settlement prices and volumes determined today for a specific future maturity.
Chapter 3 Page 3


The foreign exchange market
Foreign exchange swap markets: firms exchange or swap loans denominated in different currencies, usually for hedging purposes – acquiring a cash flow of payments in foreign currency that offsets receipts in foreign currency.

FX swaps are usually traded through a “swap dealer.”
Chapter 3 Page 4


The foreign exchange market
Options markets: a put is an option to sell foreign exchange, and a call is an option to buy foreign exchange at an exercise price at or before some future specified date.

An American style option may be exercised on or before its expiration date

A European style option cannot be exercised before expiry .
Chapter 3 Page 5

A floating exchange rate system
Supply and demand in the foreign exchange market determine the equilibrium exchange rate in a floating exchange rate system

The equilibrium rate is approximately the mid-point of the bid and ask rate, or
(bid+ask)/2

The bid is what a bank pays for a unit of foreign exchange

The ask is the price at which it sells a unit of foreign exchange
Chapter 3 Page 6

Foreign exchange quotations


Forex is quoted in two ways:
“European quote”: The foreign currency price of one dollar
“American quote”: The dollar price of a unit of foreign currency
American quotations
BID
EUR= 1.2184
ASK
1.2187
JPY= 0.009426 0.009434
GBP= 1.7669
1.7675
CHF= 0.563349 0.563507
European quotations
BID ASK
EUR= 0.8205
0.8207
JPY= 106 106.09
GBP= 0.5658
0.5660
CHF= 1.7746
1.7751

Source: SaxoBank, July 13, 2005.
As a rule of thumb, 1/bid in one quotation equals the ask in the other, and 1/ask equals the bid.
Chapter 3 Page 7



The bid-ask spread
A dealer purchases at the bid rate and sells at the offer or ask rate.
The bid-ask spread (the difference between the ask and the bid rates) represents profits to the foreign exchange dealer.
Source: Reuters, July 13, 2005.
Chapter 3 Page 8


The bid-ask spread: An example
At the bid and ask prices,
Rabobank trades 100 million euros. It buys 100 million euros at 1.2184 USD/€ and sells them at 1.2187


The bid-ask spread: 1.2187-
1.2184 = 0.0003, 3 basis points (or pips) in terms of foreign exchange
Rabobank’s dollar profits on the 100 million euros traded equal 0.0003x100,000,000 =
$30,000
Chapter 3 Page 9





A fixed exchange rate system
A fixed exchange rate system usually has a ceiling and a floor
(intervention points).
The central bank purchases dollars at the floor price and sells dollars at the ceiling to maintain the exchange rate within a band.
At 1.01 pesos per dollar, the supply exceeds the demand.
Consequently, the price falls to
1.00.
At 0.99, there is an excess demand for dollars, so the peso price of the dollar rises to 1.00, the equilibrium.
Chapter 3 Page 10




A central bank purchase of dollars
When the supply of dollars is greater than the demand for dollars at the floor price, the central bank purchases dollars at the floor price and adds them to its foreign exchange reserves.
At a floor price of 0.99 pesos per dollar, the central bank purchases
3 million dollars at 0.99 pesos per dollar. The 3 million dollars are added to central bank reserves.
The central bank could sterilize the immediate impact on the domestic money supply by selling
0.99x$3,000,000 pesos in domestic bonds on the open market.
Chapter 3 Page 11




A central bank sale of dollars
When the demand for dollars is greater than the supply of dollars at the ceiling price, the central bank draws from its reserves of dollars and sells them at the ceiling price.
The sale of reserves just equilibrates supply and demand at a price of 1.01 pesos per dollar.
Neutralization would entail a purchase of domestic bonds equal to 1.01x3,000,000 pesos.
However, the loss of dollars would continue and ultimately lead to an exchange rate crisis.
Chapter 3 Page 12



The monetary effects of Forex intervention
Sales of foreign exchange reserves automatically reduce the domestic money supply.

Neutralization or sterilization policy: a central bank buys a million dollars worth of Treasury Debt.
Purchases of foreign exchange reserves automatically increase the domestic money supply.

Neutralization or sterilization policy: a central bank sells a million dollars worth of Treasury Debt.
Chapter 3 Page 13


The euro – irrevocably fixed exchange rates
The launching of the euro €

Euro banknotes and coins have been in circulation since January 1, 2002. The 12 member states of the euro zone were
Belgium, Germany, Greece, Spain, France,
Ireland, Italy, Luxembourg, the
Netherlands, Austria, Portugal and Finland.
On January 1, 2002 previous national currencies were withdrawn from circulation.
At inception, it was worth $1.18, sank to
$0.85, and then rose to a peak of $1.35, before stabilizing somewhat at $1.25.
Chapter 3 Page 14


The euro – irrevocably fixed exchange rates
The launching of the euro €

Consequences:

Costs of conversion are disappearing.





The bid-ask spread has gone to zero for banknotes and coins, and wire transfers are less expensive.
Forex risk management is no longer necessary in the euro zone.
Exchange rate volatility is zero, so options are worthless.
European interest rates have converged since currency risk in the euro zone is eliminated.
Capital markets are enjoying lower interest rates virtually everywhere in Europe.
Chapter 3 Page 15



The SWIFT international clearing system
The Society for Worldwide Interbank
Financial Telecommunications
(SWIFT) has over a thousand members for whom it provides secure electronic transfer of monies and communication of messages internationally.
Each member bank has an electronic identification. When the bank ID is confirmed, transactions and communications can take place swiftly and securely since the computer system is a dedicated one.
Chapter 3 Page 16




Clearing House Interbank Payments System
SWIFT is connected to CHIPS (Clearing
House Interbank Payments System) in the
U.S., which handles tens of thousands of transactions and transfers billions of dollars internationally per day.
Member banks make electronic payments in
CHIP dollars during the day and at the end of the day the system nets the sums to be paid, then transfers only the net amounts.
Verification, confirmation, and authentification of transactions is also carried out by the CHIPS system .
Chapter 3 Page 17


Purchasing power parity
If a commodity can be purchased in one place and sold in another without any transport costs, tariffs, nor transactions costs, its price should be the same in both markets. This is known as the law of one
price.

E.g.: The price of the product in yen is multiplied by the spot dollar price of the yen to yield the same price in the United States.
P us

SP j or S

P us
P j
Chapter 3 Page 18


Absolute purchasing power parity
Absolute PPP states that exchange rates correspond to consumer price indices of similar commodities in each country. That is:

S

P us
P j
The spot exchange rate can be inferred from commodity prices in different markets.

That is the reasoning underlying The
Economist’s Big Mac hamburger standard.
Chapter 3 Page 19

The Big Mac Index
Chapter 3 Page 20


Arbitraging Big Macs
Arbitraging a Big Mac – buying “low” in China and selling “high” in the U.S. - has high transactions costs. The arbitrage profits are:
 
P us

1
 t us


S ask
P c

1
  us
 t c
 us


The costs of arbitrage include:





The purchase of yuan at the ask rate, .
The purchase of a Big Mac in China at .
The payment insurance and freight charges to ship
 t t c

Finally, we sell the Big Mac in the U.S., paying the sales tax there, .
Chapter 3 Page 21


The Law of One Price
For the law of one price to exactly hold, taxes, transports costs, import duties, and the bid-ask spread must all be zero.


In this case arbitrage in either direction imposes the strict law of one price, or:
P us

SP c
Clearly, the condition does not hold for nontraded goods nor goods subject to to high transport costs and tariffs.
Chapter 3 Page 22



Relative purchasing power parity
Relative PPP requires only that changes in the change exchange rate reflect the inflation rate differential between countries.
E
  t 1

S t
E
  t 1

P t us
E
  t 1

P t j
S
 us
 j t
P t
P t
The expected appreciation of the foreign currency equals the expected inflation rate at home minus the expected inflation abroad.
Chapter 3 Page 23

The monetary approach to the exchange rate
If different movements in price levels cause movements in the exchange rate, it is natural to ask what causes different inflation rates internationally.
The old view that “inflation is too much money chasing too few goods” is not far from the truth.
When money grows faster than income, prices tend to rise.
Consequently, countries that inflate their money supply relative to the supply of goods experience higher inflation and greater depreciation of their currencies.
Chapter 3
24

The monetary approach to the exchange rate
This is known as the monetary approach to the exchange rate.
The quantity theory of money states:
MV

Py where M is the money supply (currency plus checking deposits), V is the income velocity of circulation of money, P is the price level - the implicit GDP deflator - and y is real GDP.
Chapter 3
25

The monetary approach to the exchange rate
The price level is thus determined by:
P

MV y
An equivalent but insightful way of defining income velocity as the inverse of the demand for money as a fraction of income, k

1
V
Chapter 3
26

The monetary approach to the exchange rate
That is, we may express the price level as the ratio of money supply to money demand:
P

M ky where M is the money supply and ky is the demand for money.
The higher the money supply relative to money demand, the higher the price level.
Chapter 3
27

The monetary approach to the exchange rate
In terms of percentage changes over time, indicated by a dot over the variable, the rate of inflation is determined by growth in the money supply relative to growth in money demand:
  y  
V
   y   k

Inflation is caused by “too much money chasing too few goods”, compounded any acceleration in the income velocity of money,
Chapter 3
28

The monetary approach to the exchange rate
In a steady state equilibrium, the demand for money as a fraction of income remains constant, we have the simple case of inflation caused by money chasing goods:
 
Chapter 3
29

Seigniorage finance of fiscal deficits
Seigniorage finance of fiscal deficits is often known as “the printing press.”
In a sense, money is the root of all inflationary evil. It helps to understand why inflation bursts out here and there periodically.
Chapter 3
30

Seigniorage finance of fiscal deficits
To avoid inflation, any third grader as Governor of the Central Bank could follow a simple Milton
Friedman rule to maintain a low, constant rate of growth in the money supply to avoid inflation.
Chapter 3
31

Seigniorage finance of fiscal deficits
The problem is that the issue of money, seigniorage, is often the finance of last resort of the fiscal deficit.
For example, if the fiscal deficit is 10% of GDP, and 3% can be financed by borrowing at home, and 2% can be finance by borrowing abroad, the residual 5% finance must come from the “printing press” or seigniorage.
Chapter 3
32

Seigniorage finance of fiscal deficits
New money must be issued when bond finance is insufficient: dM dt


G

T

 dB
 dD
 dt dt  dB dt dD dt
In this context, is interpreted as new seigniorage.
dM dt
Chapter 3
33

Seigniorage finance of fiscal deficits
Another way of expressing inflationary finance is as the inflationary tax. multiplying and dividing the left hand side of 3.6d by M yields:
M
1
M dM dt


G

T

 dB dt
 dD dt


1
M dM dt is the percentage inflationary tax rate and M is the inflationary tax base.
Chapter 3
34

Limits to inflationary finance
There is a limit to the amount of inflationary tax since high inflation renders money a poor store of value. Consequently, money demand collapses i.e. velocity accelerates. The collapse in money demand exacerbates inflation.
Inflationary episodes - Peru in the late 1980s are often the result of collapsing real GDP, a fiscal deficit equal to 20% of GDP, financed solely my new money issue, and accelerating velocity.
Inflation made the inti worthless, so the currency had to be changed by a currency reform adopting the new sole.
Chapter 3
35

Limits to inflationary finance
Countries that rely more heavily on inflationary finance witness currency depreciation.
This suggests that purchasing power parity is founded on the growth of money supply relative to the growth of money demand.
Chapter 3
36

The monetary approach to China
China’s inflation is a puzzle. The percentage increase in China’s Consumer Price Index in 2005 was only 1.8%, despite high money growth 17.6%.
This is due to some prices being controlled, particularly fuel and gasoline.
However, the implicit price deflator, a broader measure, rose 3.4% more accurately reflecting inflation.
A strong factor keeping inflation down, in addition to 9.9% real growth in GDP, is the rise in demand for money relative to income in China, 4.3% , a sign of financial deepening in Ronald McKinnon’s terminology.
Chapter 3 37

The monetary approach to China
There is greater financial intermediation due to an income elasticity of demand for money equal nearly to 2. Here is a summary for 2005.
• Increase in Implicit GDP Deflator 3.4%,
• Increase in Money supply (Money + Quasi-
Money) 17.6%,
• Increase in Real GDP 9.9%,
• Increase in demand for money as a fraction of Nominal GDP 4.3%.
Chapter 3
38

The monetary approach to China
These results are based on an application of the monetary approach to China:
  
V
    k

Had money demand not increased relative to income by 4.3%, the inflation rate would have been 7.7%. In terms of the actual outcome:
3.4 = 17.6 - 9.9 - 4.3
Chapter 3
39

The monetary approach to China
The great advantage of the quantity theory of money is that it provides a basis for estimating the difference in expected inflation rates, thus providing the foundation for the theory of purchasing power parity.
M
S
 ky

M k
* y
*
Chapter 3
40

The monetary approach to China
That is, the level of the exchange rate is determined by the relative money supplies and money demands.
Movements in the exchange rate are due to movements in relative price levels: Thus, relative purchasing power parity as a monetary phenomenon can be expressed as:


  k

*  *  k

*

Chapter 3
41

The monetary approach to China
More rapid monetary growth at home causes the home currency to depreciate, as does less rapid real economic growth. By the same token, a fall in domestic money demand compared to foreign money demand also depreciates the home currency.
This is known as the monetary approach to the exchange rate.
Chapter 3
42

The real exchange rate
Deviations in exchange rates from purchasing power parity can, however, result from real shocks and changes in the terms of trade.
For that reason, it is useful to have a measure of the real exchange rate to capture changes in the exchange rate relative to the PPP rate. The concept of the real exchange rate is a simple one, measuring the costs of one country’s goods in terms of another’s.
Chapter 3
43

The real exchange rate
A bilateral real exchange rate is defined as:
RER

P
*
SP
Where P is the price level at home and SP* is the foreign price level expressed in terms of home currency.
When domestic prices rise relative to foreign prices, a real appreciation is said to take place.
This means home goods can buy more foreign goods because a positive deviation from purchasing power parity has taken place.
Chapter 3
44

The real exchange rate
Real dollar depreciation A dramatic example of the real depreciation of the dollar in terms of the euro has been the increase in the dollar price of the euro from $0.90 to $1.55 from 2005 to
2008, while there has been little difference in the inflation rates. The euro has thus experienced a real appreciation, while the dollar has suffered a real depreciation.
Naturally, there are many currencies, so the best
RER measurement is one that takes into account the weight of each currency in terms of trade.
The IMF provides such a calculation.
Chapter 3
45


The real effective exchange rate
The IMF’s real effective exchange rate
(RER) measures the price of a home country's goods in terms of foreign goods.





RER

100 i n


1

 where
P
S i
P i


W i

100


P
S
1
P
1


W
1


P
S
2
P
2


W
2


P
S
3
P
3


W
3
...


P
S n
P n


W n
 : the product of the i terms,
P
: the consumer price index (CPI) of the home country,
S
P
W i i i
: the home currency price of currency i ,
: the CPI in country i ,
: the currency weights of the different countries.
Chapter 3 Page 46


The real effective exchange rate
When the home country’s price rises relative to other countries, a real
appreciation takes place. It costs fewer home goods to buy foreign goods.

When foreign inflation is higher than domestic inflation, a real depreciation occurs. It costs more home goods to buy foreign goods.
Chapter 3 Page 47


Futures contracts
Futures are standardized contracts per currency traded on the floor of an organized exchange, usually Chicago or Philadelphia.





Futures have fixed maturity dates, usually less than one year.
Each future contract corresponds to a fixed amount of foreign exchange, for example 100,000 €.
Prices are determined by the Chicago method of
“open outcry”.
Initial margin is required as collateral.
The position is “marked to market” daily.
Chapter 3 Page 48







Futures contracts
Margin maintenance is required - the broker may make a “margin call” to restore margin collateral.
If not restored, the broker may liquidate the position.
A single commission is paid for the round trip purchase and sale, as well as the bid-ask spread.
There is no counterparty risk as the exchange guarantees the contracts.
Trading hours are regular exchange hours, but recently electronic trading takes place on a 24 hour basis.
While liquid, the futures market is small in size – delivery rarely takes place.
Chapter 3 Page 49


Forward contracts
Forwards, on the other hand, are any size and maturity desired, with maturities occasionally longer than a year.

For this reason, the forward market is known as the over the counter market
(OTC).

Trading occurs between firms and banks in the interbank market, with prices determined by bid ask quotes - the spread providing profits for the banks.
Chapter 3 Page 50





Forward contracts
Standing bank “relations” are necessary, but not margin collateral.
Banks are connected 24 hours a days via the
SWIFT system and negotiate forward prices directly.
In volume, the forwards market dwarfs the futures markets.
It is mainly used by firms to hedge operational exposure.
Chapter 3 Page 51




Forward contracts for hedging
International businesses hedge their risks through the forward market. Forwards give them the flexibility in terms of size of contract and maturity dates.
Forwards do not require the firm to tie up working balances in margin deposits.
In forward markets, money markets, and swap markets, there is counterparty risk, broadly defined as downgrading, either partial or complete, of the terms of financial contract.
Chapter 3 Page 52


Commodity and Forex futures
Similarities:


Futures and forward contracts are agreements to exchange an underlying asset, such as gold, at an agreed price at some future date.
Futures and forward contracts may be used either to manage risk or for speculative purposes.
Chapter 3 Page 53


Commodity and Forex futures
Differences


A forward contract is negotiated directly between counterparties and is therefore tailor-made, whereas futures contracts are standardized agreements that are traded on an exchange.
Although forward contracts offer greater flexibility, there is a degree of counterparty risk, whereas futures contracts are guaranteed by the exchange on which they are traded.
Chapter 3 Page 54


Commodity and Forex futures
Differences

Because futures contracts can be sold to third parties at any point prior to maturity, they are more liquid than forward contracts.


Futures prices are determined by the carrying costs at any time. These costs include the interest cost of borrowing gold plus insurance and storage charges.
The cost of a futures contract is determined by the "initial margin", the cash deposit that is paid to the broker.
Chapter 3 Page 55



Positions in forward contracts
A speculative position in a forward contract is the uncovered forward purchase or sale of an asset or commodity for delivery at some specified date in the future at a price, F, determined today.
A short sale may be financed by borrowing the asset from a broker to be returned later.
Chapter 3 Page 56


A short position in gold
A short position:



A short position is the sale of gold for delivery at maturity at a price
F. The short seller covers the position by buying at S in the spot market at maturity.
The profits/losses per unit of gold are F-S per metric ton, the contract unit in gold.
If the spot price of gold is greater than F the trader loses S-F per ton in covering the forward contract. If F>S, the trader gains.

The payoff for a forward sale of gold at the price F is shown by the negatively sloped line.
Chapter 3 Page 57



A short position in gold: numerical example
Suppose you sell 500 ounces of gold short for delivery in the futures market at $422 in three months. In a short sale, an investor borrows shares or gold from a brokerage firm and sells them, hoping to profit by buying them back at lower prices.
If they rise, the investor faces a loss.
Uncovered short sales are those shares or gold that have been borrowed and sold, but not yet covered by repurchase.
Chapter 3 Page 58


Gains from a short sale of gold
If the spot price falls to $400, three months later when you cover your short position, you gain $22 per ounce or $11,000.
Chapter 3 Page 59


Losses from a short sale of gold
If the price of gold rises in the spot market to $444, you lose $22 an ounce, or $11,000.
Chapter 3 Page 60


A long position in gold
A long position




A long position in gold is a purchase of gold for forward delivery.
If the spot price upon maturity is higher than the forward price, the trader gains S-F per ton.
If the spot price is less, the trader loses F-S.
The payoff is indicated by the positively sloped line.
Chapter 3 Page 61


Gains from a long position in gold
Suppose you buy 500 ounces of gold at $422 for delivery in three months, and the spot price rises to $442. You gain $20 per ounce, or
$10,000 by paying $20 per ounce below the spot price.
Chapter 3 Page 62


Losses from a long position in gold
Suppose you buy 500 ounces of gold at $422 for delivery in three months, but the spot price falls to $402. You lose $20 per ounce, or
$10,000 by paying $20 per ounce above the spot price.
Chapter 3 Page 63


A hedged position in gold
A hedged position



A hedged position is the combination of a long and a short position of the same amount and maturity of a security or asset.
What is gained on the long position is lost on the short position, and vice versa.
Graphically, the hedged position is the sum of the long and short positions, yielding the horizontal axis in the figure on the right - a zero payoff.
Chapter 3 Page 64


The cost of carry
Take the following steps:

Borrow S at interest rate r today.

Purchase one unit of a security for S today.

Sell forward at F for delivery of one unit of the security in one year.

At maturity, cash in the dividend, k, and deliver the security at the agreed upon price, F, then

Pay off the loan.
Chapter 3 Page 65


The cost of carry
The no profit arbitrage condition requires:
F

S

 r
 k

S where
 r
 k

S is the cost of carry.

In terms of percentages, the gain on the forward sale is just offset by the cost of carry:

F

S

 r
 k

The difference between the cost of borrowing and the rate of return is the cost of carry as a percent.
S
Chapter 3 Page 66




Covered interest arbitrage
It is possible to risklessly arbitrage short terms funds taking advantage of interest rate differentials in Treasuries relative to
FX discounts or premia in the forward market.
In general, if UK Treasuries pay 2% more than US Treasuries, and the forward pound is at less than a 2% discount, say 1%, an arbitrage gain can be realized, in this case,
1% .
Two percent is gained on the interest differential and one percent lost on the forward sale of the pound.
Chapter 3 Page 67

Covered interest arbitrage

To focus on strict interest rate parity – the no arbitrage profit condition - we ignore the foreign exchange and Treasury bid-ask spreads. To take advantage of small profit opportunities by arbitraging short term liquid capital, take the following two steps:
Step I. Compare dollars to dollars
1. Route one: With one million dollars, buy 90 day US Treasury bills. At maturity, they
R us

1 R us
 million dollars. Each dollar invested yields dollars – quarterly rate - in 90 days.
Chapter 3 Page 68

Covered interest arbitrage
2. Route two:
 market at S.
  three months.

1
  

 


1
 
 
R uk
  c. Sell pounds sterling in the forward market at F, yielding
F 
1

R uk

S million dollars at settlement in three months.
Chapter 3 Page 69


Covered interest arbitrage
Step II. Select the higher dollar return


1 R us


F 
1

R uk

S place short term capital in UK Treasuries due to the higher yield. That is, sell 90 day U.S.
Treasuries from your portfolio, buy pounds spot, buy U.K. 90 day Treasuries, sell the pound proceeds forward for delivery in 90 days.
You have completed a round trip and gained the covered arbitrage differential.
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
Covered interest arbitrage
Step II. Select the higher dollar return


1 R us


F 
1

R uk

S place short term capital in U.S. Treasuries due to the higher yield. That is, sell 90 day
U.K. Treasuries from your portfolio, buy dollars spot, buy U.S. 90 day Treasuries, sell the dollar proceeds forward for delivery in
90 days.
You have completed a round trip and gained the covered arbitrage differential.
Chapter 3 Page 71

Covered interest arbitrage

However, if

1

R us


F 
1

R uk

S
covered interest rate parity holds: there are no unexploited arbitrage profit opportunities, so do nothing!
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
Covered interest arbitrage
Covered interest parity can also be expressed in terms of the percentage interest rate differential versus the percentage premium or discount on the forward pound.

R us

R uk


S 
1

R uk

S which says that the interest rate differential in favor of U.S Treasuries is just (approximately) offset by the premium on the pound sterling.
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
Covered interest arbitrage
Covered interest parity can be depicted graphically: which says that on the interest rate parity line, the 1% interest rate differential in favor of U.S
Treasuries is offset by the 1% premium on the pound sterling.
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
Uncovered interest arbitrage
Uncovered interest arbitrage takes place when the exchange rate risk is not covered in the forward market. The investor sells the proceeds at the subsequent spot rate in 90 days.

Since
E
 
90

F
90
, it is generally true that expected arbitrage gains are zero when interest rate parity holds.
Chapter 3 Page 75


Uncovered interest arbitrage
An uncovered interest arbitrageur gains when the sale of foreign exchange is at a higher than expected price, for example at $1.27 rather than
$1.25.
Chapter 3 Page 76


Uncovered interest arbitrage
An uncovered interest arbitrageur loses when the sale of foreign exchange is at a lower than expected price, for example at $1.20 rather than at $1.25.
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
A foreign exchange swap
In a direct counterparty swap, a German firm borrows euros and a U.S. firm borrows dollars.
They swap the loans, the German firm servicing the dollar loan, the U.S. firm servicing the euro loan. Each firm hedges its ongoing receipts in the foreign currency at a lower borrowing rate than it could obtain by direct borrowing.
Chapter 3 Page 78









A call option – an option to buy forex
The Black-Scholes formula for the premium for a
FX call option:
C

Se
 
T
 
1

Xe
 rT
 
2 where d
1
 ln

/
 
 
2

T
/ 2

T and d
2
 d
1
 
T
C
= the value of the European style FX call option
T
= the time to option’s maturity, in years
S
= the spot price of the underlying foreign currency
X
= the option’s exercise price r
= the continuously compounded US risk-free interest rate
 = the continuously compounded foreign risk-free interest rate
 = volatility (the standard deviation of the returns on the exchange rate)
Chapter 3 Page 79


A call option – an option to buy forex
A call option has greater instrinsic value – if immediately exercised - the further it is in the money.
Chapter 3 Page 80


A put option – an option to sell forex
The Black-Scholes formula for the premium for a FX put option:
P

Xe
 rT
N
 
2

Se
 
T
N
 
1 where d
1
 ln

/
 
 
2

T
/ 2

T and d
2
 d
1
 
T







P
= the value of the European style FX put option
T
= the time to option’s maturity, in years
S
= the spot price of the underlying foreign currency
X
= the option’s exercise price r
= the continuously compounded US risk-free interest rate
 = the continuously compounded foreign risk-free interest rate
 = volatility (the standard deviation of the returns on the exchange rate)
Chapter 3 Page 81


A put option – an option to sell forex
A put option has greater instrinsic value – if immediately exercised - the further it is in the money.
Chapter 3 Page 82




Conclusion
The foreign exchange market provides for currency conversion and hedging against unanticipated changes in the exchange rate.
The resources devoted to the foreign exchange market are the bid-ask spread and commissions.
The movement toward common currency areas, such as the euro, facilitate trade in commodities and assets by reducing the transactions costs associated with different currencies.
Chapter 3 Page 83