FIN 645: International Financial Management Lecture 4 Futures and Options on Foreign Exchange

FIN 645: International Financial Management

Lecture 4

Futures and Options on Foreign Exchange

Lecture OutlineLecture Outline• Forward Market: A Recap • Futures Contracts: Preliminaries• Currency Futures Markets• Basic Currency Futures Relationships• Eurodollar Interest Rate Futures Contracts• Options Contracts: Preliminaries• Currency Options Markets• Currency Futures Options

• A forward contract is an agreement between a firm and a commercial bank to exchange a specified amount of a currency at a specified exchange rate (called the forward rate) on a specified date in the future.

• Forward contracts are often valued at $1 million or more, and are not normally used by consumers or small firms.

Forward Market: A RecapForward Market: A Recap


• When MNCs anticipate a future need for or future receipt of a foreign currency, they can set up forward contracts to lock in the exchange rate.

• The % by which the forward rate (F ) exceeds the spot rate (S ) at a given point in time is called the forward premium (p ).

F = S (1 + p )

• F exhibits a discount when p < 0.

Example: S = $1.681/£, 90-day F = $1.677/£

annualized p = F – S 360

S n

= 1.677 – 1.681 360 = –.95%

1.681 90

The forward premium (discount) usually reflects the difference between the home and foreign interest rates, thus preventing arbitrage.


• A swap transaction involves a spot transaction along with a corresponding forward contract that will reverse the spot transaction.

• A non-deliverable forward contract (NDF) does not result in an actual exchange of currencies. Instead, one party makes a net payment to the other based on a market exchange rate on the day of settlement.

Forward MarketForward Market

• An NDF (Non-Deliverable Forward Contracts) can effectively hedge future foreign currency payments or receipts:

Forward MarketForward Market

Expect need for 100M IRs. Negotiate an NDF to buy 100M IRs. on Jul 1. Reference index (closing rate quoted by India’s central bank) = $.0020/IRs.

April 1

Buy 100M IRs. from market.

July 1

Index = $.0023/ IRs. receive $30,000 from bank due to NDF.

Index = $.0018/ IRs. pay $20,000 to bank.

Currency Futures MarketCurrency Futures Market

• Currency futures contracts specify a standard volume of a particular currency to be exchanged on a specific settlement date.

• They are used by MNCs to hedge their currency positions, and by speculators who hope to capitalize on their expectations of exchange rate movements.


• The contracts can be traded by firms or individuals through brokers on the trading floor of an exchange (e.g. Chicago Mercantile Exchange), automated trading systems (e.g. GLOBEX), or the over-the-counter market.

• Brokers who fulfill orders to buy or sell futures contracts typically charge a commission.

Futures Contracts: PreliminariesFutures Contracts: Preliminaries

• A futures contract is like a forward contract:– It specifies that a certain currency will be

exchanged for another at a specified time in the future at prices specified today.

• A futures contract is different from a forward contract:– Futures are standardized contracts trading

on organized exchanges with daily resettlement through a clearinghouse.


• A major difference between a forward contract and a futures contract is the way the underlying asset is priced for future purchase or sale– A forward contract states a price for the future

transaction– By contrast, a futures contract is settled-up or

marked-to-market, daily at the settlement price– The settlement price is a price representative of

futures transaction prices at the close of daily trading on the exchange.


• A buyer of a futures contract (one who holds a long position) in which the settlement price is higher (lower) than the previous day's settlement price has a positive (negative) settlement for the day.

Futures Contracts: Futures Contracts: PreliminariesPreliminaries

• The change in settlement prices from one day to the next determines the settlement amount– Settlement amount is equal to the change

in settlement prices per unit of the underlying asset, multiplied by the size of the contract, and equals the size of the daily settlement to be added or subtracted from the margin account

– Futures trading between the long and the short is a zero-sum game

Futures Contracts: Futures Contracts: PreliminariesPreliminaries

• Standardizing Features:– Contract Size– Delivery Month– Daily resettlement

• Initial Margin (about 4% of contract value, cash or T-bills at your brokers).

Daily Resettlement: An Daily Resettlement: An ExampleExample

• Suppose you want to speculate on a rise in the $/¥ exchange rate (specifically you think that the dollar will appreciate).

Currently $1 = ¥140. The 3-month forward price is $1=¥150.

Currency per U.S. $ equivalent U.S. $

Wed Tue Wed TueJapan (yen) 0.007142857 0.007194245 140 1391-month forward 0.006993007 0.007042254 143 1423-months forward 0.006666667 0.006711409 150 1496-months forward 0.00625 0.006289308 160 159


• Currently $1 = ¥140 and it appears that the dollar is strengthening.

• If you enter into a 3-month futures contract to sell ¥ at the rate of $1 = ¥150 you will make money if the yen depreciates beyond $1 = ¥150.

• Let’s say the contract size is ¥12,500,000• Your initial margin in US dollars is 4% of the

contract value:

¥150

$10¥12,500,00.04 $3,333.33


If tomorrow, the futures rate closes at $1 = ¥149, then your position’s value drops.Your original agreement was to sell¥12,500,000 and receive $83,333.33But now ¥12,500,000 is worth $83,892.62

¥149

$10¥12,500,0062.892,83$

You have lost $559.28 overnight.


• The $559.28 comes out of your $3,333.33 margin account, leaving $2,774.05

• This is short of the $3,355.70 required for a new position.

¥149

$10¥12,500,00.04 $3,355.70

Your broker will let you slide until you run through your maintenance margin. Then you must post additional funds or your position will be closed out. This is usually done with a reversing trade.

• Enforced by potential arbitrage activities, the prices of currency futures are closely related to their corresponding forward rates and spot rates.

• Currency futures contracts are guaranteed by the exchange clearinghouse, which in turn minimizes its own credit risk by imposing margin requirements on those market participants who take a position.

Currency Futures Currency Futures MarketMarket

Comparison of the Forward & Comparison of the Forward & Futures ContractsFutures Contracts

Feature Forward Markets Futures Markets

Operational mechanism Traded directly between contracting parties

Traded on the exchanges

Contract specification Varies from trade to trade

Standardized

Counterparty risk Exists, sometimes passed on to a guarantor

Exists, But assumed by the clearing agency

Liquidation profile Low, customized and not easily accessible

High, exchange-traded

Price discovery Not efficient, scattered markets

Efficient centralized market

Quality of information dissemination

Poor, slow Good, fast

Participants Banks, brokers, Banks, brokers,MNCs. Public MNCs. Qualified

speculation not public speculationencouraged. encouraged.

Security Compensating Small securitydeposit bank balances or deposit required.

credit lines needed.Clearing Handled by Handled byoperation individual banks exchange

& brokers. clearinghouse.Daily settlementsto market prices.

Marketplace Worldwide Central exchangetelephone floor with worldwidenetwork communications.

Regulation Self-regulating CommodityFutures Trading

Commission,National Futures

Association.

Transaction Bank’s bid/ask Negotiated

Costs spread. brokerage fees.

Comparison of the Forward & Futures Comparison of the Forward & Futures ContractsContracts

Forward Contracts Futures Contracts

• Speculators often sell currency futures when they expect the underlying currency to depreciate, and vice versa.


1. Contract to sell 500,000 pesos @ $.09/peso ($45,000) on June 17.

April 4

2. Buy 500,000 pesos @ $.08/peso ($40,000) from the spot market.

June 17

3. Sell the pesos to fulfill contract.Gain $5,000.

• MNCs may purchase currency futures to hedge their foreign currency payables, or sell currency futures to hedge their receivables.


1. Expect to receive 500,000 pesos. Contract to sell 500,000 pesos @ $.09/peso on June 17.

April 4

2. Receive 500,000 pesos as expected.

June 17

3. Sell the pesos at the locked-in rate.

• Holders of futures contracts can close out their positions by selling similar futures contracts. Sellers may also close out their positions by purchasing similar contracts.


1. Contract to buy A$100,000 @ $.53/A$ ($53,000) on March 19.

January 10

3. Incurs $3000 loss from offsetting positions in futures contracts.

March 19

2. Contract to sell A$100,000 @ $.50/A$ ($50,000) on March 19.

February 15

Currency Futures MarketsCurrency Futures Markets• The Chicago Mercantile Exchange

(CME) is by far the largest. • Others include:

– The Philadelphia Board of Trade (PBOT)– The MidAmerica commodities Exchange– The Tokyo International Financial

Futures Exchange– The London International Financial

Futures Exchange

The Chicago Mercantile The Chicago Mercantile ExchangeExchange

• Expiry cycle: March, June, September, December.

• Delivery date 3rd Wednesday of delivery month.

• Last trading day is the second business day preceding the delivery day.

• CME hours 7:20 a.m. to 2:00 p.m. CST.

CME After HoursCME After Hours• Extended-hours trading on GLOBEX

runs from 2:30 p.m. to 4:00 p.m dinner break and then back at it from 6:00 p.m. to 6:00 a.m. CST.

• Singapore International Monetary Exchange (SIMEX) offer interchangeable contracts.

• There’s other markets, but none are close to CME and SIMEX trading volume.

Basic Currency Basic Currency Futures RelationshipsFutures Relationships

• Open Interest refers to the number of contracts outstanding for a particular delivery month.

• Open Interest is a good proxy for demand for a contract.

• Some refer to open interest as the depth of the market. The breadth of the market would be how many different contracts (expiry month, currency) are outstanding.

Reading a Futures QuoteReading a Futures Quote Open Hi Lo Settle Change Lifetime

High Lifetime

Low Open

Interest

Sept .6403 .6415 .6345 .6355 -.0050 .6640 .6175 51,278

Expiry monthOpening price

Highest price that day

Lowest price that dayClosing price

Daily ChangeHighest and lowest

prices over the lifetime of the

contract.

Number of open contracts

Eurodollar Interest Rate Eurodollar Interest Rate Futures ContractsFutures Contracts

• Widely used futures contract for hedging short-term U.S. dollar interest rate risk.

• The underlying asset is a hypothetical $1,000,000 90-day Eurodollar deposit—the contract is cash settled.

• Traded on the CME and the Singapore International Monetary Exchange.

• The contract trades in the March, June, September and December cycle.

Reading Eurodollar Futures Reading Eurodollar Futures QuotesQuotes

EURODOLLAR (CME)—$1 million; pts of 100%

Open High Low Settle Chg YieldSettle Change

Open Interest

June 97.58 97.65 97.59 97.64 .03 2.36 -0.3 425,705

Eurodollar futures prices are stated as an index number of three-month LIBOR calculated as F = 100-LIBOR.

The closing price for the July contract is 97.64, thus the three-month

LIBOR implied yield is 2.36 percent = 100 – 97.64

The minimum price change is one basis point. On $1 million of face value, one basis point represents $100 on an annual basis. Since it is a 3-month contract one basis point corresponds to a $25 price change.

Currency Options MarketCurrency Options Market

• Currency options provide the right to purchase or sell currencies at specified prices. They are classified as calls or puts.

• Standardized options are traded on exchanges through brokers.

• Customized options offered by brokerage firms and commercial banks are traded in the over-the-counter market.

Options Contracts: Options Contracts: PreliminariesPreliminaries

• In-the-money– The exercise price is less than the prevailing

spot price of the underlying asset.

• At-the-money– The exercise price is equal to the prevailing


• Out-of-the-money– The exercise price is more than the prevailing


• A currency call option grants the holder the right to buy a specific currency at a specific price (called the exercise or strike price) within a specific period of time.

• A call option is – in the money if exchange rate > strike

price, – at the money if exchange rate = strike

price, – out of the money

if exchange rate < strike price.

Currency Call OptionsCurrency Call Options

• Option owners can sell or exercise their options, or let their options expire.

• Call option premiums will be higher when:

• (spot price – strike price) is larger;• the time to expiration date is longer; and• the variability of the currency is greater.

• Firms may purchase currency call options to hedge payables, project bidding, or target bidding.


• Speculators may purchase call options on a currency that they expect to appreciate.

• Profit = selling (spot) price – option premium – buying (strike) price

• At breakeven, profit = 0.

• They may also sell (write) call options on a currency that they expect to depreciate.

• Profit = option premium – buying (spot) price + selling (strike) price


• A currency put option grants the holder the right to sell a specific currency at a specific price (the strike price) within a specific period of time.

• A put option is – in the money if exchange rate < strike

price, – at the money if exchange rate = strike

price, – out of the money

if exchange rate > strike price.

Currency Put OptionsCurrency Put Options

• Put option premiums will be higher when:

• (strike price – spot rate) is larger;• the time to expiration date is longer; and• the variability of the currency is greater.

• Firms may purchase currency put options to hedge future receivables.


• Speculators may purchase put options on a currency that they expect to depreciate.

• Profit =selling (strike) price – buying price – option premium

• They may also sell (write) put options on a currency that they expect to appreciate.

• Profit = option premium + selling price – buying (strike) price


• One possible speculative strategy for volatile currencies is to purchase both a put option and a call option at the same exercise price. This is called a straddle.

• By purchasing both options, the speculator may gain if the currency moves substantially in either direction, or if it moves in one direction followed by the other.

Combined Currency Put Combined Currency Put Option and Call OptionOption and Call Option

Efficiency of Efficiency of Currency Futures and OptionsCurrency Futures and Options

• If foreign exchange markets are efficient, speculation in the currency futures and options markets should not consistently generate abnormally large profits.


• European vs. American options– European options can only be exercised

on the expiration date.– American options can be exercised at

any time up to and including the expiration date.• Since this option to exercise early generally

has value, American options are usually worth more than European options, other things equal.


• Intrinsic Value– The difference between the exercise price of

the option and the spot price of the underlying asset.

• Speculative Value– The difference between the option premium

and the intrinsic value of the option.

Option Premium =

Intrinsic Value

Speculative Value

+

Currency Options MarketsCurrency Options Markets• PHLX• HKFE• 20-hour trading day.• OTC volume is much bigger than

exchange volume.• Trading is in seven major currencies

plus the euro against the U.S. dollar.

Contingency Graphs for Currency Contingency Graphs for Currency OptionsOptions

+$.02

+$.04

– $.02

– $.04

0$1.46 $1.50 $1.54

Net Profit per Unit

Future Spot Rate

For Buyer of £ Call Option

Strike price = $1.50Premium = $ .02

+$.02

+$.04

– $.02

– $.04

0$1.46 $1.50 $1.54

Net Profit per Unit

Future Spot Rate

For Seller of £ Call Option


Contingency Graphs for Currency Contingency Graphs for Currency OptionsOptions

+$.02

+$.04

– $.02

– $.04

0$1.46 $1.50 $1.54

Net Profit per Unit

Future Spot Rate

For Seller of £ Put Option


+$.02

+$.04

– $.02

– $.04

0$1.46 $1.50 $1.54

Net Profit per Unit

Future Spot Rate

For Buyer of £ Put Option


Conditional Currency Conditional Currency OptionsOptions

• A currency option may be structured such that the premium is conditioned on the actual currency movement over the period of concern.

• Suppose a conditional put option on £ has an exercise price of $1.70, and a trigger of $1.74. The premium will have to be paid only if the £’s value exceeds the trigger value.


Option Type Exercise Price Trigger Premiumbasic put $1.70 - $0.02

$1.66 $1.70 $1.74 $1.78 $1.82

$1.66

$1.68

$1.70

$1.72

$1.74

$1.76

$1.78

Ne

t A

mo

un

t R

ece

ive

d

SpotRate

BasicPut

ConditionalPut

ConditionalPut

conditional put $1.70 $1.74 $0.04


• Similarly, a conditional call option on £ may specify an exercise price of $1.70, and a trigger of $1.67. The premium will have to be paid only if the £’s value falls below the trigger value.

• In both cases, the payment of the premium is avoided conditionally at the cost of a higher premium.

Basic Option Pricing Basic Option Pricing Relationships at ExpiryRelationships at Expiry

• At expiry, an American call option is worth the same as a European option with the same characteristics.

• If the call is in-the-money, it is worth ST – E.

• If the call is out-of-the-money, it is worthless.

CaT = CeT = Max[ST - E, 0]

Currency Futures OptionsCurrency Futures Options• Are an option on a currency futures contract.• Exercise of a currency futures option results

in a long futures position for the holder of a call or the writer of a put.

• Exercise of a currency futures option results in a short futures position for the seller of a call or the buyer of a put.

• If the futures position is not offset prior to its expiration, foreign currency will change hands.

Lecture Outline (continued)Lecture Outline (continued)• Basic Option Pricing Relationships at

Expiry• American Option Pricing Relationships• European Option Pricing Relationships• Binomial Option Pricing Model• European Option Pricing Model• Empirical Tests of Currency Option Models

Basic Option Pricing Basic Option Pricing Relationships at ExpiryRelationships at Expiry

• At expiry, an American put option is worth the same as a European option with the same characteristics.

• If the put is in-the-money, it is worth E - ST.

• If the put is out-of-the-money, it is worthless.

PaT = PeT = Max[E - ST, 0]

Basic Option Profit Profiles: Call Basic Option Profit Profiles: Call BuyerBuyer


profit

loss

EE+C

ST

Long 1 call

$5

$40 $45 $55

Basic Option Profit Profiles: Call Basic Option Profit Profiles: Call BuyerBuyer


profit

loss

ST=E+CaST

Long 1 call

-Ca=-.30

67.30 70.25

E=67

At-the money

Out-of the Money

In-the Money

Basic Option Profit Profiles: Call Basic Option Profit Profiles: Call SellerSeller


profit

loss

E=67

ST=E+ Ca

STshort 1 call

-Ca=-.30

At-the Money

Options and Speculative Options and Speculative BehaviorBehavior

• Anytime the speculator believes that ST will be in excess of the breakeven point, S/he will establish a long position in the call.

• The speculator who is correct realizes a profit. If the speculator is incorrect in the forecast, the loss will be limited to the call premium.

• Alternatively, if the speculator believes that ST will be less than the breakeven point, S/he will establish a short position in the call.

• The speculator who is correct realizes a profit, the largest amount being the call premium received from the buyer. If speculator is incorrect in the forecast, very large losses may result if ST is much larger than the breakeven point.

Basic Option Profit Profiles: Basic Option Profit Profiles: Put BuyerPut Buyer

PaT = PeT = Max[E - ST, 0]

profit

loss

E=104ST= E - Pa

ST

long 1 put

-Pa=-2.47

E-Pa=104-2.47=101.53

=104-2.47=101.53

Basic Option Profit Profiles: Basic Option Profit Profiles: Put SellerPut Seller

CaT = CeT = Max[ST - E, 0]profit

loss

E=104 ST

Short 1 put

-E-Pa=104-2.47=101.53

ST= E - Pa

Pa=2.47

Options and Speculative Options and Speculative BehaviorBehavior

• Anytime the speculator believes that ST will be less than the breakeven point, S/he will establish a long position in the put.

• The speculator who is correct realizes a profit. If the speculator is incorrect in the forecast, the loss will be limited to the call premium.

• Alternatively, if the speculator believes that ST will in excess of the breakeven point, S/he will establish a short position in the put.

• The speculator who is correct realizes a profit, the largest amount being the put premium received from the buyer. If speculator is incorrect in the forecast, very large losses may result if ST is much smaller than the breakeven point.

American Option Pricing American Option Pricing RelationshipsRelationships

• With an American option, you can do everything that you can do with a European option—this option to exercise early has value.

CaT > CeT = Max[ST - E, 0]

PaT > PeT = Max[E - ST, 0]

Market Value, Time Value and Intrinsic Market Value, Time Value and Intrinsic Value for an American CallValue for an American Call

CaT > Max[ST - E, 0]

Profit

loss

E ST

Market ValueOf the Option

Intrinsic value

S T - E

Time value

Out-of-the-money In-the-money

European Option Pricing European Option Pricing RelationshipsRelationships

Consider two investments1 Buy a call option on the British pound

futures contract. The cash flow today is -Ce

2 Replicate the upside payoff of the call by 1 Borrowing the present value of the exercise

price of the call in the U.S. at i$ The cash flow today is E /(1 + i$)

2 Lending the present value of ST at i£ The cash flow is - ST /(1 + i£)

European Option Pricing RelationshipsEuropean Option Pricing RelationshipsIllustrationIllustration

Current Time Expiration ST ≤E ST >E

• Portfolio A:Buy Call -Ce 0 ST-E Lend PV of E in US -E/(1+r$) E E_________________________________________________________Total -Ce-E/(1+r$) E ST

• Portfolio B:Lend PV of 1 unit of foreign currencyi at rate ri -St/(1+ri) ST ST

• It follows that Portfolio A has an equal value as that of Portfolio B when ST >E

• However, Portfolio A has a higher value when ST ≤E.


When the option is in-the-money both strategies have the same payoff.

When the option is out-of-the-money it has a higher payoff the borrowing and lending strategy.

Thus: 0,

)1()1(max

$£

i

E

i

SC T

e


Using a similar portfolio to replicate the upside potential of a put, we can show that:

0,)1()1(

max£$

i

S

i

EP T

e

Binomial Option Pricing Binomial Option Pricing ModelModel

• Imagine a simple world where the dollar-euro exchange rate is S0($/ ) = $1 today and in the next year, S1($/ ) is either $1.1 or $.90.

$1

$.90

$1.10

S0($/ ) S1($/ )


$1

$.90

$1.10

S0($/ ) S1($/ )

$.10

$0

C1($/ )

A call option on the euro with exercise price S0($/ ) = $1 will have the following payoffs.


• The most important lesson from the binomial option pricing model is:

the replicating portfolio intuition.the replicating portfolio intuition.

Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.

European Option Pricing European Option Pricing FormulaFormula

• We can use the replicating portfolio intuition developed in the binomial option pricing formula to generate a faster-to-use model that addresses a much more realistic world.


The model isTredNEdNFC $)]()([ 210

Where

C0 = the value of a European option at time t = 0

TrrteSF )( £$

r$ = the interest rate available in the U.S.

r£ = the interest rate available in the foreign country—in this case the U.K.

,5.)/ln( 2

1T

TEFd

Tdd 12


Find the value of a six-month call option on the British pound with an exercise price of $1.50 = £1The current value of a pound is $1.60The interest rate available in the U.S. is r$ = 5%.

The interest rate in the U.K. is r£ = 7%.The option maturity is 6 months (half of a year).The volatility of the $/£ exchange rate is 40% p.a.Before we start, note that the intrinsic value of the option is $.10—our answer must be at least that.


Let’s try our hand at using the model. If you have a calculator handy, follow along.

Then, calculate d1 and d2

106066.05.4.

5.)4.0(5.)50.1/485075.1ln(5.)/ln( 22

1

T

TEFd

First calculate 485075.150.1 50.0)07.05(.)( £$ eeSF Trr

t

176878.05.4.106066.012 Tdd


N(d1) = N(0.106066) = .5422

N(d2) = N(-0.1768) = 0.4298TredNEdNFC $)]()([ 210

157.0$]4298.50.15422.485075.1[ 5.*05.0 eC

485075.1F

106066.01 d

176878.02 d

Option Value DeterminantsOption Value Determinants

Call Put1. Exchange rate + –2. Exercise price – +3. Interest rate in U.S. + –4. Interest rate in other country + –5. Variability in exchange rate+ +6. Expiration date + +

The value of a call option C0 must fall within

max (S0 – E, 0) < C0 < S0.

The precise position will depend on the above factors.

Empirical TestsEmpirical TestsThe European option pricing model

works fairly well in pricing American currency options.

It works best for out-of-the-money and at-the-money options.

When options are in-the-money, the European option pricing model tends to underprice American options.

Documents

FIN 645: International Financial Management Lecture 4 Futures and Options on Foreign Exchange