Foreign Exchange Options Prof. Ian Giddy New York University.

Foreign Exchange Options

Prof. Ian Giddy

New York University

Copyright ©1996 Ian H. Giddy Currency Options 2

Tools for Hedging

Petrobras has to pay for equipment from Japan, in Japanese yen, in 3 monthsLock in a forward priceOr use a call option on the Yen?How much will it cost?


Option Hedge

CALL

OPTION

ON YEN

FORWARD

CONTRACT


Option Hedge

Questions about options: When should companies use them? Which options? How much do they cost, Are they worth paying for? What is the risk to the bank?


Foreign Exchange Options

The right, but not the obligation, to exchange currency at a predertermined rate.

The right to buy is a call; the right to sell, a put.

American options permit the holder to exercise at any time before the expiration date; European options, only on the expiration date.


Hockey Stick Diagrams

These show payoff at expiration of options. Eg. buying a call produces a gain if the currency rises above the strike plus the premium; the call writer’s profit profile is opposite.

Gain

or Loss

Buy a Put

Value of Swiss franc


Option Payoff Diagrams

Buy call: right to purchase foreign currency

Buy put: right to sell foreign currency

Profit

ForwardRate

+

0

_

BUYCALLOPTION

Strike

Premium

Profit

Forward

+

0

_SELLCALLOPTION

Profit

Forward

+

0

_

BUYPUTOPTION

Profit

Forward

+

0

_SELLPUTOPTION

Figure 2. Payoff at Expiration of Options. Eg. buying a call produces a gain if the currency (ie the futures price) risesabove the strike plus the premium; the call writer's profit profile is opposite.


Pricing a Call Option

Forward relative to strike Time to expiration Volatility Interest rate

Option

Value

Currency Value


Option Price is

“Present value of average-profit-given exercise

Underlying instrument has probability distribution

Probability of exercise is given by area under curve to right of strike price

Average-profit-given-exercise is mean of right hand area under curve minus the strike price (you buy at strike and sell at market)

Value of option is the present value of that profit


Value of Call Option

Equals present value of its expected intrinsic value at expiration, given that the forward is above the strike

FORWARD

STRIKE


Value of Call Option

INTRINSIC VALUE TIME VALUE

EXPECTED VALUE OF PROFIT

GIVEN EXERCISE

STRIKE

FORWARDSHADED AREA:

Probability distribution

of the log of the forward

rate on the expiration date

for values above the strike.


Currency Option Pricing: the Famous Formula

C PV FN d KN d

where

dF K

d d

[ ( ) ( )]

ln( / )

1 2

1

2 1

2


Forwardmarket priceof currency

Profit(gain or loss)

+

0

_

K F

K F

Time Value

F-K

Time Value

E(FJ *FJ >K)

How a Change in the Forward Rate Changes the Currency Option’s Price


Delta Hedging

OptionValue

Forward orFuturesPrice

HEDGERATIO=50%

HEDGERATIO=80%

HEDGERATIO=15%


The Effect of Increased Volatility

Forwardmarket priceof currency

Profit(gain or loss)

+

0

_

K F

K F

Time Value

F-K

Time Value

E(FJ *FJ >K)


Gain

or Loss

Value of Swiss franc

Plus:

Buy a put

Betting on Volatility

Net effect:

Long Straddle

Buy a Call


Unconventional OptionsCan be Cheaper

Examples Asian Knock-in Knock-out Digital Lookback

These are priced using binomial models

2.562.54

2.52 2.552.5 2.53

2.51 2.542.52

2.53

Soles per US Dollar


Asian (Average Price) Options

Pays the difference between the strike price on the expiry date and the average price of the underlying instrument over a certain time period.

Used where the purchaser wants to cover many spot transactions using one hedging instrument.

Since the volatility of an average is less than the volatility for a spot price, average price options are less expensive


STRIKE PRICE

AVERAGE PRICE


Knock-in and Knock-out Options

A knock-in option has the same payout as a standard option if a certain barrier level is reached before the option expiry date, otherwise it pays nothing.

A knock-out option becomes worthless if the price of the underlying instrument reaches a barrier level before the option expiry date. If the barrier is not reached, the payout is the same as a standard option.


BARRIER

STRIKE PRICE


Client Situations...

View on:Direction of ratesVolatility of ratesRelative rates

Constraints - internal or imposed Credit aspects.


View on Direction, Volatility or Both?


When Use What?

View on direction View on volatility

Direction:

Volatility

Currencyrising

Currencyfalling

No trend

Volatilityincreasing

Buy call Buy put Buystraddle

Volatilityfalling

Sell put Sell call Sellstraddle

No trend involatility

Buyforward

Sellforward

Arbitrage

Foreign Exchange Options Prof. Ian Giddy New York University.

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