International FinanceFINA 5331

Lecture 14:

Hedging currency risk with currency options

Aaron Smallwood Ph.D.

Currency options

– An options contract can be bought/sold not only over the counter, but also on a centralized exchange. In the case of an options contract, there are several centralized exchanges including the Philadelphia Stock Exchange.

– Options contracts bought and sold on exchanges are only available in certain currencies. In particular, an options contract is available for Australian dollars, British pounds, Canadian dollars, euros, Japanese yen, and Swiss franc (all against the $) on the Philadelphia Stock Exchange.

– Options contracts bought and sold on exchanges are only sold in fixed lots. In particular, on the Philadelphia Stock Exchange, currency options are available in the following denominations:

• A$ 10,000 £10,000• C$ 10,000 €10,000• ¥ 1,000,000 CHF 10,000

Currency options…continued

– Currency options sold on a centralized exchange have specific delivery dates. In particular, a currency option bought or sold on the Philadelphia Stock Exchange matures on the Friday before the third Wednesday of the expiration month. Contracts on the exchange have a trading cycle of March, June, September, and December with two additional near term monthly contracts. This implies that if it is November, then there will be options contracts available in the next two months (December and January).

– Unlike a forward contract, the culmination of the contract need not result in delivery of currency. For example, if an options contract is purchased in Canadian $, the trader never has to take delivery of Canadian $ as a result of the contract if they don’t wish to. In other words, the trader has the right, but not the obligation to take delivery of currency in the future. The trader will only use the option if the movements in future exchange rates make it profitable or cost-efficient to do so.

– Today, the Philadelphia stock exchange offers pure dollar settled contracts.

Speculating with put options

• Consider a trader that wishes to short yen. They can use a put option. Suppose they have access to an August put with a strike price of 100.00 (all contracts are listed as cents per unit of foreign currency…except ¥, which is listed as cents per 100 units of foreign currency). Trader wishes to sell ¥10,000,000 (e.g. 10 contracts).

• This is a risky strategy (implies a depreciation of the yen relative to the current exchange rate). Suppose when the contract matures, S($/¥)=$0.0092. Trader WINS…How?

Profit

• With put option, we exercise when future exchange rate is LESS than strike price.– We sell ¥10,000,000 at $0.01.– Problem, where do we get yen?

• Buy them in the spot market at $0.0092.• We still have to pay the premium. Suppose the

premium is $0.000255

– Total profit: – (0.01-0.0092-.000255)* ¥10,000,000=

$5,450.

Illustration

Q - What is the maximum gain for one put option?A - $9,745 = ¥1,000,000×($0.01 – $0.000255)or $10,000 - $255 = $9,745.00

Q - At what exchange rate do you break even?A - $0.01-$0.000255=$0.009745

0.01

Future Spot Rate

Profit

loss

$9,745

$0.009745

–$255.00

Hedging with call options

• Consider a US importer that buys goods from Germany for delivery in three months. The US trader owes €1,000,000 at the time of delivery.

• The trader cares about the cost in US dollars. The trader is concerned that the euro will appreciate in value. The trader could purchase a call option.

• Suppose the trader selects the call option with a strike price of 129.

Scenario #1

• Suppose on August 17, the dollar price of the euro ends up being $1.23.

• The options expires “out of the money.” The trader will not exercise the option.

• The trader must pay the premium:– .0094*1,000,000=9,400– Total cost of purchasing euros:

$1,230,000+9,400=$1,239,400.– For any exchange rate less than or equal to 1.29, the

trader will lose because they have to pay the full premium amount.

Scenario #2

• Suppose the dollar price of the euro ends up being $1.40. The trader is much better off with the option.

• The option is exercised. The trader would prefer to buy at $1.29

• They will still the pay the premium amount.– With an option the trader will pay $1,290,000 +

$9,400=$1,299,400.– Without an option, the trader would have paid

$1,400,000.– The option saved the trader $1,400,000-

$1,299,400=100,600

Scenario 3

• Suppose the exchange rate ends up being $1.2955. The trader exercises the option.

• In spite of using the option, the trader would have actually been better without one.

• With the option, the trader would prefer to buy euros at $1.29.

• They lose the premium amount no matter what.• The total cost anytime the trader exercises the

option is $1,299,400.• In this case, without the option, the trader would

only have paid $1,295,500.

Graphical illustration