I _ Let r be the domestic interest rate, rf be the foreign interest rate and t be the time period. For where Fc the spot price It IS known that in the a curency, the forward pnce is Foe binomial model for pricing options on foreign cunencies, the factors for up and down movements in the pnce are respectively given by u = e(r-r') where is the volatility (a) By using the fonnulae for u and d given above and based on nsk-neutral argument, *rive the probability of an up movement. A financial institution has just sold Euopean put options on the Sterling pound which matures in nine months. Suppose that the spot exchange rate is I .45 dollars per Sterling pounct the exercise price is I dollars Sterling potuzd, and assuming continuous compounding, the risk-free interest rate in the United States is 50/0 per annum, the risk-free interest rate in Blitain is 6% per anmun, and the volatility of the exchange rate is 30% per annum (b) Use palt (a) and a three-step binomial tree to find the price of the European put option. (c) If the put option is American find the optimal time step to exercise the option.