Foreign Exchange Options

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Presentation transcript:

Foreign Exchange Options Prof. Ian Giddy New York University

Tools for Hedging Petrobras has to pay for equipment from Japan, in Japanese yen, in 3 months Lock in a forward price Or use a call option on the Yen? How much will it cost?

Option Hedge

Option Hedge FORWARD CONTRACT

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. Buy a Put Gain or Loss Value of Swiss franc

Option Payoff Diagrams Buy call: right to purchase foreign currency Buy put: right to sell foreign currency

Put-Call Parity Gain or Loss Value of DM Buy a Call Plus: Short the currency Net effect: Buy a put Value of DM

Option Combinations Four classic ways of combining an option with a futures to create the opposite option

Put-Call Parity Gain or Loss Value of Swiss franc Sell a Call Plus: Buy a put Net effect: Short the currency Value of Swiss franc

Put-Call Parity Buying a call and selling a put can replicate a long futures From this we get put-call parity for foreign exchange: Thus if we know the put’s price, we can get the call’s price, and vice-versa

Put-Call Parity: Carmen’s Career Calculate a put price, given a call price of $0.01 and futures=$0.35.30, at strike of $0.36: P =1.00-(35.30-36)/(1+0.0755)148/360 =1.68 cents per DM (Locking in off-market futures: Fee =(36-35.30)/(1+0.0755)148/360 = .68 cents/DM)

Forward relative to strike Time to expiration Volatility Interest rate 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 FORWARD Equals present value of its expected intrinsic value at expiration, given that the forward is above the strike STRIKE

EXPECTED VALUE OF PROFIT Value of Call Option SHADED AREA: Probability distribution of the log of the forward rate on the expiration date for values above the strike. FORWARD STRIKE INTRINSIC VALUE TIME VALUE EXPECTED VALUE OF PROFIT GIVEN EXERCISE

Currency Option Pricing: the Famous Formula

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

Delta Hedging

The Effect of Increased Volatility

Betting on Volatility Gain or Loss Value of Swiss franc Buy a Call Plus: Buy a put Net effect: Long Straddle Value of Swiss franc

Unconventional Options Can be Cheaper Examples Asian Knock-in Knock-out Digital Lookback These are priced using binomial models 2.56 Soles per US Dollar 2.54 2.52 2.55 2.5 2.53 2.51 2.54 2.52 2.53

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

AVERAGE PRICE STRIKE 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

Constraints - internal or imposed Credit aspects. Client Situations... View on: Direction of rates Volatility of rates Relative rates Constraints - internal or imposed Credit aspects.

View on Direction, Volatility or Both?

When Use What? View on direction View on volatility

www.giddy.org Ian Giddy NYU Stern School of Business Tel 212-998-0332; 917-930-0291 Fax 212-995-4233; 630-604-7413 ian.giddy@nyu.edu http://www.giddy.org