A bank was expecting to receive $100,000 from a loan issued to the Spanish government. Since Spain has problems repaying the loan immediately, the bank extends the loan for another year at the same interest rate of 10 percent. However, in the rescheduling agreement, the bank reserves the right to exercise an option for receiving the payment in British pounds, equal to €87,813, converted at the current exchange rate of €0.7983/$.
a. If the cost of funds to the bank is also assumed to be 10 percent, what is the value of this option built into the agreement if only two possible exchange rates are expected at the end of the year, €0.8467/$ or €0.7499/$, with equal probability?
b. How would your answer differ, if the probability of the exchange rate being €0.8467/$ is 70 percent and that of €0.7499/$ is 30 percent?
c. Does the currency option have more or less value as the volatility of the exchange rate increases?