# Question

1. Assume that the spot price of the British pound is $1.55, the 30-day annualized sterling interest rate is 10%, the 30-day annualized U.S. interest rate is 8.5%, and the annualized standard deviation of the dollar:pound exchange rate is 17%. Calculate the value of a 30-day PHLX call option on the pound at a strike price of $1.57.

2. Suppose the spot price of the yen is $0.0109, the threemonth annualized yen interest rate is 3%, the three-month annualized dollar rate is 6%, and the annualized standard deviation of the dollar:yen exchange rate is 13.5%. What is the value of a three-month PHLX call option on the Japanese yen at a strike price of $0.0099/¥?

Option pricing stems from application of the most productive idea in all of finance-arbitrage. The idea underlying arbitrage pricing of a new asset is simple: Create a portfolio of assets with known market prices that exactly duplicates the distribution of payoffs of the new asset. The price of the new asset must equal the cost of purchasing the mimicking portfolio.

Otherwise, arbitrageurs would earn riskless profits. This is the technique used by Fischer Black and Myron Scholes in developing the Black-Scholes option pricing model.4 In order to develop a closed-form solution for the pricing of a currency option, we must make some assumptions about the statistical properties of the spot and forward exchange rates. Assuming that both these exchange rates are lognormally distributed (i.e., that their natural logarithm follows a normal distribution), one can duplicate the price of a European call option exactly, over a short time interval, with a portfolio of domestic and foreign bonds. This portfolio can be represented as

C(t) = aS(t)B*(t, T) + bB(t, T) .... (8A.1)

2. Suppose the spot price of the yen is $0.0109, the threemonth annualized yen interest rate is 3%, the three-month annualized dollar rate is 6%, and the annualized standard deviation of the dollar:yen exchange rate is 13.5%. What is the value of a three-month PHLX call option on the Japanese yen at a strike price of $0.0099/¥?

Option pricing stems from application of the most productive idea in all of finance-arbitrage. The idea underlying arbitrage pricing of a new asset is simple: Create a portfolio of assets with known market prices that exactly duplicates the distribution of payoffs of the new asset. The price of the new asset must equal the cost of purchasing the mimicking portfolio.

Otherwise, arbitrageurs would earn riskless profits. This is the technique used by Fischer Black and Myron Scholes in developing the Black-Scholes option pricing model.4 In order to develop a closed-form solution for the pricing of a currency option, we must make some assumptions about the statistical properties of the spot and forward exchange rates. Assuming that both these exchange rates are lognormally distributed (i.e., that their natural logarithm follows a normal distribution), one can duplicate the price of a European call option exactly, over a short time interval, with a portfolio of domestic and foreign bonds. This portfolio can be represented as

C(t) = aS(t)B*(t, T) + bB(t, T) .... (8A.1)

## Answer to relevant Questions

What is an interest rate swap? What is the difference between a basis swap and a coupon swap?At time t, 3M borrows ¥12.8 billion at an interest rate of 1.2%, paid semiannually, for a period of two years. It then enters into a two-year yen/dollar swap with Bank of America (BA) on a notional principal amount of $100 ...What alternative hedging transactions are available to a company seeking to hedge the translation exposure of its German subsidiary? How would the appropriate hedge change if the German affiliate's functional currency were ...General Electric recently had to put together a $50-million bid, denominated in Swiss francs, to upgrade a Swiss power plant. If it won, GE expected to pay subcontractors and suppliers in five currencies. The payment ...Madison Inc. imports olive oil from Chilean firms, and the invoices are always denominated in pesos (Ch$). It currently has a payable in the amount of Ch$250 million that it would like to hedge. Unfortunately, there are no ...Post your question

0