20.Options

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Hedging with Foreign Currency

Options

By Soeren HansenBy Soeren Hansen

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What is an Option? A Currency Option is an option, butA Currency Option is an option, but notnot an obligation toan obligation to

buy or sell currency during a specified time period (timebuy or sell currency during a specified time period (timeto maturity, T) at a specified price (exercise/strike price,to maturity, T) at a specified price (exercise/strike price,

X)X) The price or value of the option is called the premium, PThe price or value of the option is called the premium, P

Two different Options:Two different Options:

1.1. Call OptionCall Option2.2. Put OptionPut Option

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What is a Call -and a Put Option?

A currency Call option is an option but notA currency Call option is an option but not

an obligation toan obligation to buybuy currency during acurrency during a

specified time period at a specified pricespecified time period at a specified price

A currency Put option is an option but notA currency Put option is an option but not

an obligation toan obligation to sellsell currency during acurrency during aspecified time period at a specified pricespecified time period at a specified price

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What is an European -and an American Option?

An European currency option is an option,An European currency option is an option,

which can be exercisedwhich can be exercised onlyonly on theon the

maturity datematurity date

An American currency option is an optionAn American currency option is an option

which can be exercisedwhich can be exercised any timeany time prior toprior tothe maturity datethe maturity date

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Why an Option? Since the the holder of a Currency OptionSince the the holder of a Currency Option

has the right but not the obligation to tradehas the right but not the obligation to trade

currency, it is beneficial to use options tocurrency, it is beneficial to use options tohedge potential transactions (ex. bids nothedge potential transactions (ex. bids not

yet accepted)yet accepted)

The exercise/strike price and the premiumThe exercise/strike price and the premiumtogether determine the the floor or ceilingtogether determine the the floor or ceiling

established for the potential transactionestablished for the potential transaction

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Call Option The Call Option establishes a ceiling for the exchange rate, andThe Call Option establishes a ceiling for the exchange rate, and

the option can be used to hedge foreign currency outflowsthe option can be used to hedge foreign currency outflows(potential payments)(potential payments)

If S>XIf S>X=> Profit increases one=> Profit increases one--forfor--one with appreciation of the foreignone with appreciation of the foreigncurrency. At (X+P) the holder of the option breaks even (ceilingcurrency. At (X+P) the holder of the option breaks even (ceiling

price)price)

If S The call option will not be exercised, because the holder isbetter off buying the foreign currency in the spot market. Thebetter off buying the foreign currency in the spot market. The

holder will have a negative profit reflecting the premium, Pholder will have a negative profit reflecting the premium, P

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Profit Profile for a Call Option

Profit

S

-P

X X+P

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Put Option The Put Option establishes a floor for the exchange rate, and theThe Put Option establishes a floor for the exchange rate, and the

option can be used to hedge foreign currency inflowsoption can be used to hedge foreign currency inflows

If S>XIf S>X

=> The call option will not be exercised, because the holder is=> The call option will not be exercised, because the holder isbetter off selling the foreign currency in the spot market. Thebetter off selling the foreign currency in the spot market. Theholder will have a negative profit reflecting the premium, Pholder will have a negative profit reflecting the premium, P

If S Profit increases one--forfor--one with depreciation of the foreignone with depreciation of the foreign

currency. At (Xcurrency. At (X--P) the holder of the option breaks even (floorP) the holder of the option breaks even (floorprice)price)

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Profit Profile for a Put Option

Profit

S

-P

XX-P

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Option Pricing For European optionsFor European options

Black Black--Scholes pricing modelScholes pricing model

Garman & KohlhagenGarman & Kohlhagen For both European and American option:For both European and American option:

Binomial pricing modelBinomial pricing model

Implicit finite difference methodImplicit finite difference method

I willI will notnot go into these different pricing models, but for thego into these different pricing models, but for theinterested student see John C. Hull interested student see John C. Hull Options, Futures and otherOptions, Futures and otherderivativesderivatives

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Principles of pricing currency options

The value of an option on its maturity date isThe value of an option on its maturity date is

either its immediate exercise value or zero,either its immediate exercise value or zero,

whichever is higherwhichever is higher If two options are identical in all respects with theIf two options are identical in all respects with the

exception of the exercise price, aexception of the exercise price, a callcall option with aoption with a

higher exercise price will always have a lowerhigher exercise price will always have a lower

value and avalue and a putput option with a higher exercise priceoption with a higher exercise pricewill always have a greater value than thewill always have a greater value than the

corresponding options with lower exercise pricescorresponding options with lower exercise prices

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If two American options are identical in allIf two American options are identical in all

respects with exception of the length of therespects with exception of the length of the

contract, the longer contract will have a greatercontract, the longer contract will have a greatervalue at all times (more flexible)value at all times (more flexible)

Prior to expiration, an American option has aPrior to expiration, an American option has a

value at least as large as the correspondingvalue at least as large as the corresponding

European option (more flexible)European option (more flexible)

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A larger (positive) difference between theA larger (positive) difference between the

domestic and foreign interest rate (idomestic and foreign interest rate (i i*),i*),

increases the price of a call and decreases the priceincreases the price of a call and decreases the priceof a put (expected appreciation of the homeof a put (expected appreciation of the home

currency)currency)

The value of the option increases as the volatilityThe value of the option increases as the volatility

of the underlying currency increasesof the underlying currency increases

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Example B.Lack & S.Choles Enterprises of Salem, OR importsB.Lack & S.Choles Enterprises of Salem, OR imports

French wine. The wine is really rare, so B.Lack &French wine. The wine is really rare, so B.Lack &

S.Choles have to bid for the wine. On November 2S.Choles have to bid for the wine. On November 2ndnd

B.Lack & S.Choles bidsB.Lack & S.Choles bids 62,500, but the firm will not62,500, but the firm will not

know until December 15know until December 15thth whether the bid is accepted orwhether the bid is accepted or

not. Recently the dollar tanked against the euro, so tonot. Recently the dollar tanked against the euro, so to

protect against a further appreciation of the euro, the firmprotect against a further appreciation of the euro, the firm

purchases apurchases a 62,500 call option. The strike price is 1.275062,500 call option. The strike price is 1.2750$/$/ and the option premium is one cent pr. euro. Theand the option premium is one cent pr. euro. The

ceiling price is therefore 1.2850 $/ceiling price is therefore 1.2850 $/, for a maximum, for a maximum

payment of $80,312.5payment of $80,312.5

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Example If the euro appreciates to 1.3000 $/If the euro appreciates to 1.3000 $/, the payment, the payment

without the option would be $81,250, so B.Lack &without the option would be $81,250, so B.Lack &

S.Choles will exercise the option and purchase theS.Choles will exercise the option and purchase theeuro for 1.2750, which is a payment of $79,687.5euro for 1.2750, which is a payment of $79,687.5

+ premium of $625+ premium of $625

If the euro depreciates to 1.2000, B.Lack &If the euro depreciates to 1.2000, B.Lack &

S.Choles will be better of buying euro on the spotS.Choles will be better of buying euro on the spotmarket, so they let the option expire unused. Themarket, so they let the option expire unused. The

payment is then $75,000 + premium of $625payment is then $75,000 + premium of $625

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Questions?

Thank youThank you

20.Options

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