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 buy foreign

currency. – A put option is an option to sell foreign

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 buy foreign

currency. – A put option is an option to sell foreign

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.

• A European option can 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.

Philadelphia Exchange Options

Philadelphia Exchange Options

Spot rate, 88.15 ¢/€

Size of contract:€62,500

Exercise price0.90 ¢/€

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/€)Option price for

purchase of €1 at 90¢ is 1.25 ¢

Maturity month

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.

-$0.90

-$0.75

-$0.60

-$0.45

-$0.30

-$0.15

$0.00

$0.15

$0.30

$0.45

$0.60

$0.75

$0.90

$0.0

0

$0.1

0

$0.2

0

$0.3

0

$0.4

0

$0.5

0

$0.6

0

$0.7

0

$0.8

0

$0.9

0

$1.0

0

$1.1

0

$1.2

0

$1.3

0

$1.4

0

$1.5

0

$1.6

0

$1.7

0

$1.8

0

Spot Rate at Expiration

Val

ue o

f F

orw

ard/

Cal

l Opt

ion

at E

xpir

atio

n .

Value of Forward Buy at Expiration

Value of Call at Expiration

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

$8,000,000

0.8 0.85 0.9 0.95 1

Spot Price

Val

ue o

f 10

mill

ion

euro

s

If you also buy a put option with a strike price of .90 for .01, your underlying position looks like this.

$8,800,000

$9,000,000

$9,200,000

$9,400,000

$9,600,000

$9,800,000

$10,000,000

0.8 0.85 0.9 0.95 1

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)