7 Futures and Options on Foreign Exchange

7/29/2019 7 Futures and Options on Foreign Exchange

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INTERNATIONAL

FINANCIAL

MANAGEMENT

EUN / RESNICK

Fifth Edition

Copyright 2009 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin


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Chapter Objective:

This chapter discusses exchange-traded currency

futures contracts, options contracts, and options on

currency futures.

7Chapter SevenFutures and Options

on Foreign Exchange

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Chapter Outline

Futures Contracts: Preliminaries

Currency Futures Markets

Basic Currency Futures Relationships Eurodollar Interest Rate Futures Contracts

Options Contracts: Preliminaries

Currency Options Markets Currency Futures Options

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Chapter 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

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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 onorganized exchanges with daily resettlement

through a clearinghouse.

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Standardizing Features:

Contract Size

Delivery Month

Daily resettlement

Initial performance bond (about 2 percent of

contract value, cash or T-bills held in a street

name at your brokerage).

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Daily Resettlement: An Example

Consider a long position in the CME Euro/U.S.

Dollar contract.

It is written on125,000 and quoted in $ per.

The strike price is $1.30 the maturity is 3

months.

At initiation of the contract, the long posts an

initial performance bond of $6,500.

The maintenance performance bond is $4,000.

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Recall that an investor with a long position gainsfrom increases in the price of the underlying asset.

Our investor has agreed to BUY125,000 at

$1.30 per euro in three months time. With a forward contract, at the end of three

months, if the euro was worth $1.24, he wouldlose $7,500 = ($1.24$1.30) 125,000.

If instead at maturity the euro was worth $1.35,the counterparty to his forward contract wouldpay him $6,250 = ($1.35$1.30) 125,000.

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With futures, we have daily resettlement of

gains an losses rather than one big settlement at

maturity.

Every trading day:

if the price goes down, the long pays the short

if the price goes up, the short pays the long

After the daily resettlement, each party has a

new contract at the new price with one-day-

shorter maturity.

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Performance Bond Money

Each days losses are subtracted from theinvestors account.

Each days gains are added to the account.

In this example, at initiation the long posts aninitial performance bond of $6,500.

The maintenance level is $4,000.

If this investor loses more than $2,500 he has adecision to make: he can maintain his long positiononly by adding more fundsif he fails to do so, hisposition will be closed out with an offsetting shortposition.

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Over the first 3 days, the euro strengthens thendepreciates in dollar terms:

$1,250

$1,250

$1.31

$1.30

$1.27 $3,750

Gain/LossSettle

= ($1.31$1.30)125,000$7,750

$6,500

$2,750

Account Balance

= $6,500 + $1,250

On third day suppose our investor keeps his long

position open by posting an additional $3,750.

+ $3,750 = $6,500

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Over the next 2 days, the long keeps losing moneyand closes out his position at the end of day five.

$1,250

$1,250

$1.31

$1.30

$1.27$1.26

$1.24

$3,750$1,250

$2,500

Gain/LossSettle

$7,750

$6,500

$2,750 + $3,750 = $6,500$5,250

$2,750

Account Balance

= $6,500$1,250

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Toting Up

At the end of his adventures, our investor hasthree ways of computing his gains and losses:Sum of daily gains and losses

$7,500 = $1,250$1,250$3,750$1,250$2,500Contract size times the difference between initialcontract price and last settlement price.

$7,500 = ($1.24/$1.30/) 125,000

Ending balance on account minus beginning balance onaccount, adjusted for deposits or withdrawals.

$7,500 = $2,750 ($6,500 + $3,750)

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Total loss =$7,500

$1,250

$1,250

$1.31

$1.30

$1.27

$1.26

$1.24

$3,750

$1,250

$2,500

Gain/LossSettle

$7,750

$6,500

$2,750 + $3,750

$5,250

$2,750

Account Balance

= $2,750($6,500 + $3,750)

$$1.30 $6,500

= ($1.24$1.30) 125,000

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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

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The Chicago Mercantile Exchange

Expiry cycle: March, June, September,

December.

Delivery date third 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.

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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.

The Singapore Exchange offers interchangeable

contracts.

There are other markets, but none are close to

CME and SIMEX trading volume.

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Reading Currency Futures Quotes

OPEN HIGH LOW SETTLE CHG

OPEN

INT

Euro/US Dollar (CME)125,000; $ per

1.4748 1.4830 1.4700 1.4777 .0028Mar 172,396

1.4737 1.4818 1.4693 1.4763 .0025Jun 2,266

Highest price that day

Lowest price that day

Closing price

Daily Change

Number of open contracts

Expirymonth

Opening price

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Basic Currency Futures Relationships

Open Interestrefers 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.

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Notice that open interest is greatest in the nearby contract,in this case March, 2008.

In general, open interest typically decreases with term to

maturity of most futures contracts.


OPEN

INT


1.4748 1.4830 1.4700 1.4777 .0028Mar 172,396

1.4737 1.4818 1.4693 1.4763 .0025Jun 2,266

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Basic Currency Futures Relationships

The holder of a long position is committing himself to pay

$1.4777 per euro for125,000a $184,712.50 position.As there are 172,396 such contracts outstanding, this

represents a notational principal of over $31.8 billion!


OPEN

INT


1.4748 1.4830 1.4700 1.4777 .0028Mar 172,396

1.4737 1.4818 1.4693 1.4763 .0025Jun 2,266

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1 + i

1 + i$ F($/)

S($/)=

Recall from chapter 6, our interest rate parity condition:


OPEN

INT


1.4748 1.4830 1.4700 1.4777 .0028Mar 172,396

1.4737 1.4818 1.4693 1.4763 .0025Jun 2,266

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From March to June 2008 we should expect lower interestrates in dollar denominated accounts: if we find a higher rate in

a euro denominated account, we may have found an arbitrage.


OPEN

INT


1.4748 1.4830 1.4700 1.4777 .0028Mar 172,396

1.4737 1.4818 1.4693 1.4763 .0025Jun 2,266

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Eurodollar Interest Rate


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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 depositthe contract is cashsettled.

Traded on the CME and the Singapore

International Monetary Exchange. The contract trades in the March, June, September

and December cycle.

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Reading Eurodollar Futures Quotes

Eurodollar futures prices are stated as an index number of three-month

LIBOR calculated as F= 100LIBOR.

The closing price for the June contract is 96.56 thus the implied yield is

3.44 percent = 10096.56

Since it is a 3-month contract one basis point corresponds to a $25 price

change: .01 percent of $1 million represents $100 on an annual basis.


OPEN

INTYLD CHG

Eurodollar (CME)1,000,000; pts of 100%

96.56 96.58 96.55 96.56 - 3.44 -Jun 1,398,959

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An option gives the holder the right, but not the

obligation, to buy or sell a given quantity of an

asset in the future, at prices agreed upon today.

Calls vs. Puts

Call options gives the holder the right, but not the

obligation, to buy a given quantity of some asset at

some time in the future, at prices agreed upon today. Put options gives the holder the right, but not the

obligation, to sell a given quantity of some asset at

some time in the future, at prices agreed upon today.

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European vs. American options

European options can only be exercised on the

expiration date.

American options can be exercised at any time up toand 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.

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In-the-money

The exercise price is less than the spot price of the

underlying asset.

At-the-money The exercise price is equal to the spot price of the

underlying asset.

Out-of-the-money The exercise price is more than the spot price of the

underlying asset.

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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+

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Currency Options Markets

PHLX

HKFE

20-hour trading day.

OTC volume is much bigger than exchange

volume.

Trading is in six major currencies against the

U.S. dollar.

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PHLX Currency Option


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PHLX Currency Option

Specifications

Currency Contract Size

Australian dollar AD10,000

British pound 10,000Canadian dollar CAD10,000

Euro 10,000

Japanese yen 1,000,000Swiss franc SF10,000

http://www.phlx.com/products/xdc_specs.htm

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Basic Option Pricing
http://www.phlx.com/products/http://www.phlx.com/products/


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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 STE.

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

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

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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 worthE - ST.

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

PaT= PeT=Max[EST, 0]

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Basic Option Profit Profiles

E

ST

Profit

loss

c0 E+ c0

Long 1 call

If the call is in-the-

money, it is worth

ST

E.If the call is out-of-

the-money, it is

worthless and the

buyer of the call

loses his entire

investment ofc0. In-the-moneyOut-of-the-money

Owner of the call

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E

ST

Profit

loss

c0

E+ c0

short 1

call

If the call is in-the-

money, the writer

loses STE.

If the call is out-of-

the-money, the writer

keeps the option

premium.

In-the-moneyOut-of-the-money

Seller of the call

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E

ST

Profit

loss

p0

Ep0 long 1 put

Ep0

If the put is in-

the-money, it is

worthEST.

The maximum

gain isEp0

If the put is out-

of-the-money, it

is worthless and

the buyer of theput loses his

entire investment

ofp0.Out-of-the-moneyIn-the-money

Owner of the put

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E

ST

Profit

loss

p0

Ep0 short 1 put

E + p0

If the put is in-

the-money, it is

worthEST. The

maximum loss is

E + p0

If the put is out-

of-the-money, it

is worthless and

the seller of theput keeps the

option premium

ofp0.

Seller of the put

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Example

$1.50

ST

Profit

loss

$0.25

$1.75

Long 1 call

on 1 pound

Consider a call

option on31,250.

The option premium

is $0.25 per

The exercise price is

$1.50 per.

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Example

$1.50

ST

Profit

loss

$7,812.50

$1.75

Long 1 call

on31,250

Consider a call

option on31,250.

The option premium

is $0.25 per The exercise price is

$1.50 per.

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Example

$1.50

ST

Profit

loss

$42,187.50

$1.35 Long 1 puton31,250

Consider a put

option on31,250. The option premium

is $0.15 per

The exercise price is

$1.50 per euro.

What is the maximum gain on this put option?

At what exchange rate do you break even?

$4,687.50

$42,187.50 = 31,250($1.50 $0.15)/

$4,687.50 = 31,250($0.15)/7-39

American Option Pricing


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p g

Relationships

With an American option, you can do

everything that you can do with a European

option AND you can exercise prior to expiry

this option to exercise early has value, thus:

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

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

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Market Value, Time Value and Intrinsic


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Market Value, Time Value and IntrinsicValue for an American Call

E

ST

Profit

loss

Long 1 callThe red line shows thepayoff at maturity, not

profit, of a call option.

Note that even an out-

of-the-money option

has valuetime value.

Intrinsic value

Time value

In-the-moneyOut-of-the-money

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European Option Pricing


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p p g

Relationships

Consider two investments1 Buy a European call option on the British pound

futures contract. The cash flow today isCe

2 Replicate the upside payoff of the call by1 Borrowing the present value of the dollar exercise

price of the call in the U.S. at i$E

(1 + i$)The cash flow today is

2 Lending the present value ofSTat iST

(1 + i)The cash flow today is

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Relationships

When the option is in-the-money both strategieshave the same payoff.

When the option is out-of-the-money it has a

higher payoff than the borrowing and lendingstrategy.

Thus:

Ce>Max

ST E

(1 + i) (1 + i$) , 0

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Relationships

Using a similar portfolio to replicate the upside

potential of a put, we can show that:

Pe>MaxSTE

(1 + i)(1 + i$) , 0

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The Hedge Ratio


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The Hedge Ratio

This ratio gives the number of units of the underlyingasset we should hold for each call option we sell inorder to create a riskless hedge.

The hedge ratio of a option is the ratio of change in

the price of the option to the change in the price ofthe underlying asset:

H =C CS1 S1

downup

downup

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Hedge Ratio

This practice of the construction of a riskless

hedge is called delta hedging.

The delta of a call option is positive.

The delta of a put option is negative.

Deltas change through time.

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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.7-47


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Currency Futures Options

Why a derivative on a derivative?

Transactions costs and liquidity.

For some assets, the futures contract can have

lower transactions costs and greater liquiditythan the underlying asset.

Tax consequences matter as well, and for someusers an option contract on a future is more taxefficient.

The proof is in the fact that they exist.

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7 Futures and Options on Foreign Exchange

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