FIN 645: International Financial Management

Lecture 4

Futures and Options on Foreign Exchange

Lecture 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

Forward Market: A Recap

• 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 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.

Forward Market: A Recap

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

annualized p = F – S

S



360

n

= 1.677 – 1.681

1.681



360 90 = –.95%

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

Forward Market

• 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 Market

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

April 1 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.

July 1 Buy 100M IRs. from market.

Index = $.0023/ IRs.



receive $30,000 from bank due to NDF. Index = $.0018/ IRs .



pay $20,000 to bank.

Currency Futures Market

• Currency futures contracts specific settlement date.

specify a standard volume of a particular currency to be exchanged on a • They are used by MNCs to hedge their currency positions, and by speculators who hope to capitalize on their expectations of exchange rate movements.

Currency Futures Market

• 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: 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.

Futures Contracts: Preliminaries

• 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.

Futures Contracts: Preliminaries

• 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: Preliminaries

• 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: Preliminaries

• 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 Example

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

Japan (yen)

1-month forward 3-months forward 6-months forward

Currency per U.S. $ equivalent Wed Tue

0.007142857

U.S. $

0.007194245

Wed

140

Tue

139 0.006993007

0.006666667

0.00625

0.007042254

0.006711409

0.006289308

143 150 160 142 149 159 Currently $1 = ¥140. The 3-month forward price is $1=¥150.

Daily Resettlement: An Example

• 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: $3,333.33

 .04

 ¥12,500,00 0  $1 ¥150

Daily Resettlement: An Example

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 $83,333.33

But now ¥12,500,000 is worth $83,892.62

$ 83 , 892 .

62  ¥12,500,00 0  $1 ¥149

You have lost $559.28 overnight.

Daily Resettlement: An Example

• 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.

$3,355.70

 .04

 ¥12,500,00 0  $1 ¥149  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

.

Currency Futures Market

• 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.

Comparison of the Forward & Futures Contracts

Feature Forward Markets Futures Markets Operational mechanism Contract specification Counterparty risk Liquidation profile Price discovery Quality of information dissemination Traded directly between contracting parties Varies from trade to trade Exists, sometimes passed on to a guarantor Low, customized and not easily accessible Not efficient, scattered markets Poor, slow Traded on the exchanges Standardized Exists, But assumed by the clearing agency High, exchange-traded Efficient centralized market Good, fast

Comparison of the Forward & Futures Contracts

Forward Contracts Futures Contracts Participants Security deposit Clearing operation Marketplace Regulation Transaction Costs Banks, brokers,

MNCs. Public speculation not encouraged.

Compensating

bank balances or credit lines needed.

Handled by

individual banks & brokers.

Worldwide

telephone network

Self-regulating Bank’s bid/ask

spread.

Banks, brokers,

MNCs. Qualified public speculation encouraged.

Small security

deposit required.

Handled by

exchange clearinghouse.

Daily settlements to market prices.

Central exchange

floor with worldwide communications.

Commodity

Futures Trading Commission, National Futures Association.

Negotiated

brokerage fees.

Currency Futures Market

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

April 4 1. Contract to sell 500,000 pesos @ $.09/peso ($45,000) on June 17.

June 17 2. Buy 500,000 pesos @ $.08/peso ($40,000) from the spot market.

3. Sell the pesos to fulfill contract.

Gain $5,000.

Currency Futures Market

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

April 4 June 17 1. Expect to receive 500,000 pesos. Contract to sell 500,000 pesos @ $.09/peso on June 17. 2. Receive 500,000 pesos as expected.

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

Currency Futures Market

• 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.

January 10 1. Contract to buy A$100,000 @ $.53/A$ ($53,000) on March 19.

February 15 2. Contract to sell A$100,000 @ $.50/A$ ($50,000) on March 19.

March 19 3. Incurs $3000 loss from offsetting positions in futures contracts.

Currency 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 Exchange

• 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 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 Futures 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 Quote

Open Hi Lo Settle Change Lifetime High Lifetime Low Open Interest Sept

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

Closing price Lowest price that day Highest and lowest prices over the lifetime of the contract.

Highest price that day Opening price Expiry month Number of open contracts

Eurodollar Interest Rate Futures 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 Quotes

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

Open High Low Settle Chg Yield Settle Change Open Interest

June

97.58

97.65

97.59

97.64

.03

2.36

-0.3

Eurodollar futures prices are stated as an index number of three 425,70 5 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 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: Preliminaries

• 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 spot price of the underlying asset.

• Out-of-the-money – The exercise price is more than the prevailing spot price of the underlying asset.

Currency Call Options

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

in the money at the money out of the money if exchange rate > strike price, if exchange rate = strike price, if exchange rate < strike price.

Currency 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.

Currency Call Options

• 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

Currency Put Options

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

in the money at the money if exchange rate < strike price, if exchange rate = strike price, out of the money if exchange rate > strike price.

Currency 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.

Currency Put Options

• 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

Combined Currency Put Option and Call Option

• 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.

Efficiency of Currency Futures and Options

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

Options Contracts: Preliminaries

• 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.

Options Contracts: Preliminaries

• 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 = Intrinsic Premium Value + Speculative Value

Currency 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 Options

For Buyer of £ Call Option For Seller of £ Call Option Strike price = $1.50

Premium = $ .02

Strike price = $1.50

Premium = $ .02

Net Profit per Unit +$.04

Net Profit per Unit +$.04

+$.02

+$.02

Future Spot Rate 0 0 – $.02

– $.04

$1.46

$1.50

$1.54

Future Spot Rate – $.02

– $.04

$1.46

$1.50

$1.54

Contingency Graphs for Currency Options

For Buyer of £ Put Option For Seller of £ Put Option Strike price = $1.50

Premium = $ .03

Strike price = $1.50

Premium = $ .03

Net Profit per Unit +$.04

Net Profit per Unit +$.04

+$.02

Future Spot Rate +$.02

0 0 – $.02

– $.04

$1.46

$1.50

$1.54

– $.02

– $.04

$1.46

$1.50

$1.54

Future Spot Rate

Conditional Currency Options

• 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.

Conditional Currency Options

Option Type basic put conditional put Exercise Price $1.70

$1.70

Trigger $1.74

Premium $0.02

$0.04

Basic Put $1.78

$1.76

$1.74

$1.72

$1.70

$1.68

$1.66

Conditional Put Conditional Put $1.66

$1.70

$1.74

$1.78

$1.82

Spot Rate

Conditional Currency Options

• 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 Relationships 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

S T

– E.

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

C aT

= C

eT

= Max[S

T

- E, 0]

Currency 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)

• 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 Relationships 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 - S T

.

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

P aT

= P

eT

= Max[E - S

T

, 0]

Basic Option Profit Profiles: Call Buyer

C aT = C eT

= Max[S

T

- E, 0] profit $5 loss

E

$40

E+C

$45 $55

S T

Basic Option Profit Profiles: Call Buyer

C aT = C eT

= Max[S

T

- E, 0] profit -Ca= .30

loss Out-of the Money E=67 At-the money

S T = E+Ca

67.30

70.25

In-the Money

S T

Basic Option Profit Profiles: Call Seller

C aT = C eT

= Max[S

T

- E, 0] profit -Ca= .30

S T = E +

Ca

E=67 S T

loss At-the Money

Options and Speculative Behavior

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

T • 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. will be in • Alternatively, if the speculator believes that S T 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 S is much larger than the breakeven point. T

Basic Option Profit Profiles: Put Buyer

P aT = P eT

= Max[E - S

T

, 0] E-P a =104 2.47=101.53

profit

S T

-P a =-2.47

loss

S T= E P a

=104-2.47=101.53

E=104

Basic Option Profit Profiles: Put Seller

profit

C aT = C eT

= Max[S

T

- E, 0] P a =2.47

S T= E P a E=104 S T

-E-P a =104-2.47=101.53

loss

Options and Speculative Behavior

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

T • 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. will be • Alternatively, if the speculator believes that S T 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 S is much smaller than the breakeven point. T

American Option Pricing Relationships

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

C aT P aT

> C

eT

= Max[S

T

- E, 0] > P

eT

= Max[E - S

T

, 0]

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

C aT

> Max[S

T

- E, 0] Profit

Market Value Of the Option

Time value Intrinsic value Out-of-the-money

E

In-the-money

S T

loss

European Option Pricing Relationships

Consider two investments 1 Buy a call option on the British pound futures contract. The cash flow today is -C

e

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 S

T

flow is - S

T

/(1 + i £ at i £ The cash )

• • • • European Option Pricing Relationships Illustration

Current Time Expiration

S T ≤E S T >E

Portfolio A:

Buy Call Lend PV of E in US _________________________________________________________ Total -C e -C e -E/(1+r -E/(1+r $ ) $ ) 0 S T E S T E E E

Portfolio B:

Lend PV of 1 unit of foreign currency i at rate r i -S t /(1+r i ) S T S T

It follows that Portfolio A has an equal value as that of Portfolio B when S T >E

However, Portfolio A has a higher value when S T ≤E.

European Option Pricing Relationships

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:

C e

 max    ( 1

S



T i

£ )  ( 1

E i

$ ) , 0   

European Option Pricing Relationships

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

P e

 max   

E

( 1 

i

$ )  ( 1

S T



i

£ ) , 0   

Binomial Option Pricing Model

• Imagine a simple world where the S 0 dollar-euro exchange rate is S ) = $1 today and in the next year, S 1 S 1 ($/ ) 0 ($/ $1.10

$1 $.90

Binomial Option Pricing Model

 A call option on the euro with exercise price S 0 ($/ ) = $1 will have the following payoffs.

S 0 ($/ ) S 1 ($/ ) $1.10

C 1 ($/ ) $.10

$1 $.90

$0

Binomial Option Pricing Model

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

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 Formula

• 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.

European Option Pricing Formula

The model is Where

C

0  [

F



N

(

d

1 ) 

E



N

(

d

2 )]

e



r

$

T C

0 = the value of a European option at time

t

= 0

F r

$ 

e

(

r

$ 

r

£ )

T S t

= the interest rate available in the U.S.

r

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

d

1  ln(

F

/ 

E

)  .

5 

T

2

T

,

d

2 

d

1  

T

European Option Pricing Formula

Find the value of a six-month call option on the British pound with an exercise price of $1.50 = £1 The current value of a pound is $1.60

The 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.

European Option Pricing Formula

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

First calculate

F



S t e

(

r

$ 

r

£ )

T

 1 .

50

e

(.

05  .

07 ) 0 .

50  1 .

485075 Then, calculate

d

1 and

d

2

d

1  ln(

F

/ 

E

)  .

5  2

T T

 ln( 1 .

485075 / 1 .

50 )  .

5 ( 0 .

4 ) 2 .

5  0 .

106066 .

4 .

5

d

2 

d

1  

T

 0 .

106066  .

4 .

5   0 .

176878

European Option Pricing Formula

F

 1 .

485075

d

1  0 .

106066

d

2   0 .

176878

N

(

d

1 ) =

N

(0.106066) = .5422

N

(

d

2 ) =

N

(-0.1768) = 0.4298

C

0  [

F



N

(

d

1 ) 

E



N

(

d

2 )]

e



r

$

T C

0  [ 1 .

485075  .

5422  1 .

50  .

4298 ]

e

 .

05 * .

5  $ 0 .

157

Option Value Determinants

– 1.

2.

3.

4.

– 5.

+ 6.

Exchange rate Exercise price Interest rate in U.S.

Call + – + – Put + Interest rate in other country + Variability in exchange rate + Expiration date + + The value of a call option C 0 within must fall max (S – E, 0) < C < S .

Empirical Tests

The 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.