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## Foreign Currency Options

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**Foreign Currency Options**• A foreign currency option is a contract giving the option purchaser (the buyer) • the right, but not the obligation, • to buy or sell a given amount of foreign exchange at a fixed price per unit • for a specified time period (until the expiration date).**Foreign Currency Options**• There are two basic types of options: • A call option is an option to buyforeign currency. • A put option is an option to sellforeign currency. • A buyer of an option is termed the holder; the seller of an option is referred to as the writer or grantor.**Foreign Currency Options**• There are two basic types of options: • A call option is an option to buyforeign currency. • A put option is an option to sellforeign currency. • A buyer of an option is termed the holder; the seller of an option is referred to as the writer or grantor.**Foreign Currency Options**• An American option gives the buyer the right to exercise the option at any time between the date of writing and the expiration or maturity date. • AEuropean optioncan be exercised only on the expiration date, not before.**Currency Options Markets**• December 10th, 1982, the Philadelphia Stock Exchange introduced currency options. Growth has been spectacular. • OTC currency options are not usually traded and can only be exercised at maturity (European). Used to tailor specific amounts and expiration dates.**Spot rate, 88.15 ¢/€**Size of contract:€62,500 Exercise price0.90 ¢/€ Maturity month Option price for purchase of €1 at 90¢ is 1.25 ¢ Philadelphia Exchange Options The indicated contract price is: €62,500 $0.0125/€ = $781.25 One call option gives the holder the right to purchase€62,500 for $56,250 (= €62,500 $0.90/€) One call option gives the holder the right to purchase€62,500 for $56,250. This option costs $781.25.**Reading the WSJ Currency Options Table**• The option prices are for the purchase or sale of one unit of a foreign currency with U.S. dollars. For the Japanese yen, the prices are in hundredths of a cent. For other currencies, they are in cents. • Thus, one call option contract on the Euro with exercise price of 90 cents and exercise month January would give the holder the right to purchase Euro 62,500 for U.S. $56,250. The indicated price of the contract is 62,500 0.0125 or $781.25. • The spot exchange rate on the Euro on 12/15/00 is 88.15 cents per Euro.**Value of Call Option versus Forward Position at Expiration**A call option allows you to obtain only the “nice part” of the forward purchase.**Call Option Value at Expiration**• To summarize, a call option allows you to obtain only the “nice part” of the forward purchase. Rather than paying X for the foreign currency (as in a forward purchase), you pay no more than X, and possibly less than X.**Option Premiums and Option Writing**• Likewise, a firm that expects to receive future Euro might acquire a put option on Euro. • The right to sell at X ensures that this firm gets no less than X for its Euro. • Thus, buying a put is like taking out an insurance contract against the risk of low exchange rates.**Option Premiums and Option Writing**• Like any insurance contract, the insured party will pay an insurance premium to the insurer (the writer of the option). • The price of an option is often called the option premium and acquiring an option contract is called buying an option. • As with ordinary insurance contracts, the option premium is usually paid up-front.**Using Currency Options to Hedge Currency Risk**Suppose you expect to receive 10,000,000 euros in 6 months. Without hedging, your underlying position looks like this**If you also buy a put option with a strike price of .90 for**.01, your underlying position looks like this.**Pricing Options**• Consider a euro call option that has a strike price of .90 and that is selling for .04. • If the spot price is .93, the option must be worth at least .03. This is called the intrinsic value of the option. • If the option is selling for more than the intrinsic value, the difference (in the example, .04-.03=.01) is called the time value. We might just as well call it the hope value, since it represents the owners hope that the spot price will go up by even more.**Pricing Options**• Consider a euro call option that has a strike price of .90 and that is selling for .04. • If the spot price is .93, the option must be worth at least .03. This is called the intrinsic value of the option. • If the option is selling for more than the intrinsic value, the difference (in the example, .04-.03=.01) is called the time value. We might just as well call it the hope value, since it represents the owners hope that the spot price will go up by even more.**We think about volatility in prices as being a bad thing,**and for most financial assets this is true. A stock whose price fluctuates wildly is less desireable (all other things the same) than a more stable stock. But an interesting thing about options is that their value is actually enhanced by volatility of the underlying asset value. • Suppose you owned a euro call option with a strike price of .90. • Imagine that you thought there was a 50% chance the euro would fall to .87 and a 50% chance you thought the euro would increase to .93 before expiration of the contract. This means there is a 50% chance that you will make .03. • Imagine now that you changed your mind and decided there was a 50% chance the euro would fall to .85 and a 50% chance you thought the euro would increase to .95 before expiration of the contract. You now believe there is a 50% chance you will make .05 and so you should be willing to pay more for the option.**Pricing Options: the role of interest rates**• Consider two different investment portfolios • Portfolio “A” consists of • A bond that will pay X at maturity • The bond costs X/(1+rus) where rus is the US interest rate • A call option with a strike price of X • The option will pay S-X if S>X and 0 if S<X • The option costs C • Thus • If St<X, you get X • If St>X, you get St-X+X =St**Portfolio “B” is made up by**• Making a loan of S0/(1+rforeign) units of the foreign currency, where S0 is the current spot rate and rforeign is the foreign interest rate. • When the loan matures, you get St units of the domestic currency. A bond that will pay X at maturity**Conclude: Portfolio A is better than Portfolio B (A never**returns less than X and B returns less than X if St<X) • But this implies that B can never sell for more than A • That is • C+X/(1+rus) > S0/(1+rforeign) • or • C> S0/(1+rforeign)-X/(1+rus)