Suppose the spot exchange rate is $1.22 per British pound and the strike on a dollar denominated pound put is $1.20.Assume r = 0.04,rf = 0.05,σ = 0.20 and the option expires in 270 days.What is the put option price?

Question

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The put option price is $0.075. This is because the put option gives the holder the right to sell one British pound for $1.20 at any time before the option expires. Since the spot exchange rate is $1.22 per British pound, the holder of the put option would only exercise the option if the exchange rate falls below $1.20. The probability of this happening is given by the Black-Scholes formula, which is a function of the spot exchange rate, the strike price, the risk-free interest rate, the foreign interest rate, the volatility of the exchange rate, and the time to expiration. In this case, the Black-Scholes formula gives a probability of 0.341 that the exchange rate will fall below $1.20 before the option expires. This means that the expected value of the put option is $0.075, which is the probability of the option being exercised multiplied by the profit that would be made if the option is exercised.

Suppose the Spot Exchange Rate Is $1