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For a five-period binomial model price on the same options, the call is worth \$26.37, while the put is worth \$11.08. With 200 periods, the call price is \$25.94, and the put price is \$10.65. (The calculations for the binomial model are not shown here, but similar calculations for other options appear later in this chapter.)

Options on Foreign Currency

We now explore the application of the Merton model to pricing options on a foreign currency. We assume that we are looking at the issues from the point of view of a U.S. options trader. In terms of the Merton model, the dollar value of the foreign currency takes the role of the stock price, S„ and the foreign interest rate takes the role of the continuous dividend rate, 6. The standard deviation in the Merton model is that of the underlying asset, so the correct standard deviation to use in the model is the standard deviation of the foreign currency.

As an example, consider a European call and a European put option on the British pound. The pound is currently worth \$1.40, and has a standard deviation of 0.5, reflecting difficulties in the European Monetary System (EMS). The current British risk-free rate is 12 percent, while the U.S. rate is 8 percent. The call and put both have a striking price of \$1.50 per pound, and they both expire in 200 days.

According to the Merton model, the call is worth \$0.1452, while the put value is \$0.2700. Both of these prices are the dollar price for an option on a single British pound. We illustrate the computation of the price of the currency options using a five-period binomial model. The binomial parameters are:

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