Foreign Currency Options

Chapter Seven

Eiteman, Stonehill, and Moffett

04/22/23 1Chapter Seven - Derivatives

Hedging vs speculation firms hedge

make money on their core competency reduce risk writing a covered option

firms do not speculate options are not a core competency speculation tries to make a return from

risk

04/22/23 2Chapter Seven - Derivatives

Quick review forward contracts Negotiable contracts

Price, forward rate is contracted Amount, how much foreign exchange will

be exchange for domestic currency Term, when delivery will be made

Contract is deliverable according to terms Will not be able to get out of the

contract04/22/23 Chapter Seven - Derivatives 3

Currency futures contracts standardized contract terms

amount of foreign exchange standardized $ 100,000 Canadian, £ 62.500, Peso 500,000, ¥ 12,500,00, Euro 1,000,000

exchange rate fixed at contract time delivery dates standardized by the exchange

March, June, September, December 6 mos Chicago Mercantile Exchange

contracts expire two business days prior to the 3rd Wednesday of the delivery month

Contract is reversible

04/22/23 4Chapter Seven - Derivatives

Futures contracts Short position (selling a future)

Fix price to deliver fx @ 1.0337 To deliver 100,000 cd Delivery Dec 15, 2007

Long position (buying a future) Fix priced to take delivery fx @ 1.0337 To take delivery 100,000 cd

04/22/23 Chapter Seven - Derivatives 5

Market makers in currency futures international monetary market (IMM) London international financial futures

exchange (LIFFE) Chicago Mercantile Exchange New York mercantile exchange Singapore international monetary

exchange (SIMEX)

04/22/23 6Chapter Seven - Derivatives

Trading specifics commissions small (less than 0.5%) margin requirements typically 2% to

3% contracted amount both sides of contract guaranteed by

exchange contracts marked to market daily

04/22/23 7Chapter Seven - Derivatives

long one June euro contract contracted June delivery of 1,000,000

Euros spot price 0.9737 / dollar or 0.9737 *

1,000,000 = 973,700 usd at contract initial margin paid in when contracted

e.g. 2% on Euro contract 20,000 usd maintenance margin

e.g. 1% on Euro contract 10,000 usd

04/22/23 8Chapter Seven - Derivatives

marking to market 1st day e.g. tomorrows settlement price 0.9817

(0.9817 - 0.9737) * 1,000,000 = 8,000 futures price is now 0.9817

long the future (wanting euros) margin account = 20,000 - 8,000 = 12,000

short the future (wanting dollars) margin account = 20,000 + 8,000 = 28,000

04/22/23 9Chapter Seven - Derivatives

marking to market 2nd day e.g., next days settlement price 0.9867

(0.9867 - 0.9817) * 1,000,000 = 5,000 futures price is now 0.9867

long the future (wanting euros) margin account = 12,000 - 5,000 = 7,000 margin call - buyer of the future must bump up

his margin short the future (wanting dollars)

margin account = 28,000 + 5,000 = 33,000

04/22/23 10Chapter Seven - Derivatives

Futures contract expires (long side of contract) e.g. last settlement price 1.0017

net change in margin (1.0017 - 0.9737) * 1,000,000 = 28,000

final futures price 1.0017 long the future (wanting euros)

net change in margin account + 28,000

pays ( -1,001,700 + 28,000) = -973,700 dollars

receives +1,000,000 euros04/22/23 11Chapter Seven - Derivatives

Futures contract expires(short side of contract) last settlement price 1.0017

net change in margin (0.9737 - 1.0017) * 1,000,000 = -28,000

final futures price 1.0017 short the future (wanting dollars)

net change in margin account -28,000 pays -1,000,000 euros receives (1,001,777 - 28,000) = 973,700

dollars

04/22/23 12Chapter Seven - Derivatives

Futures marking to market reduces(illimanates)

default risk daily resettlement confines risk to one day’s

price movements large daily movements in price will result in

trading halt margin call during trading halt

trader want to terminate the contract will take the opposite contract if long two contracts, will go short two contracts

cost is the interest paid on margins

04/22/23 13Chapter Seven - Derivatives

Comparison to forwards forward contracts

flexible higher default risk fixed into contract Must deliver on expiration

futures contracts standardized much lower default risk reversible

04/22/23 14Chapter Seven - Derivatives

Options - characteristics American option can be exercised

anytime up to the expiration date European option can only be exercise

at the expiration date in-the-money - option which if

exercised will make money out-of-the-money - option which if

exercised will lose money

04/22/23 15Chapter Seven - Derivatives

Options - types Call option

option to buy currency fixed price (exercise price, strike price) expiration date

Put option option to sell currency fixed price (exercise price, strike price) expiration date

04/22/23 16Chapter Seven - Derivatives

Over-the-counter Market written by banks

usd against pounds, euros, cd, yen usually written in round lots;

1, 2, 3, 5, 10 million banks willing to write variable options

amount exercise (strike) price maturity date

less liquid than traded option04/22/23 17Chapter Seven - Derivatives

Options on organized exchanges Standardized contracts

amount fixed maturity dates

Auction markets Philadelphia exchange London International Financial Futures

Exchange

04/22/23 18Chapter Seven - Derivatives

Options - over-the-counter Market written by banks

usd against pounds, euros, cd, yen usually written in round lots;

1, 2, 3, 5, 10 million banks willing to write variable options

amount exercise (strike) price maturity date

less liquid than traded option

04/22/23 19Chapter Seven - Derivatives

Call characteristics e exchange rate x exercise price sdx standard deviation of exchange

rate

04/22/23 20Chapter Seven - Derivatives

Long a call option

e

c

x

Call out of the moneywhen e < x

Call in the moneywhen e > x

04/22/23 21Chapter Seven - Derivatives

Short the Call Option

C

SX

04/22/23 22Chapter Seven - Derivatives

Market Value of the Call

),,,( , rfet kxsdeCC

0eC

0

C

0

esdC

0xC

0

rfkC

04/22/23 23Chapter Seven - Derivatives

Valuation exercise price (negative) exchange rate (positive) volatility (positive) term to maturity (positive) risk-free rate of return (positive)

04/22/23 24Chapter Seven - Derivatives

Value of the Exercised Call

0)(,

),(

0,

0,

,

CnxeCxeIf

ormoneytheofout

PxeIf

ttx

t

txt

04/22/23 25Chapter Seven - Derivatives

Long a call option

e

c

x

exercised valueof the call

market valueof the call

04/22/23 26Chapter Seven - Derivatives

Long a put option

e

P

x

Call out of the moneywhen e > x

Call in the moneywhen e < x

04/22/23 27Chapter Seven - Derivatives

Short the Put Option

PSX

04/22/23 28Chapter Seven - Derivatives

Market Value of the Put

),,,( , rfet kxsdePP

0eP 0

P

0

esdP 0

xP

0

rfkP

04/22/23 29Chapter Seven - Derivatives

Value of the Exercised Put

0)(,

),(

0,

0,

,

PnexPxeIf

ormoneytheofout

PxeIf

ttx

t

txt

04/22/23 30Chapter Seven - Derivatives

Long the Put Option

P

SX

04/22/23 31Chapter Seven - Derivatives