The dollar interest rate is 5% (continuously compounded) and the yen rate is 1% (continuously compounded).
Consider an at-the-money American dollar call that is yen-denominated (i.e., the call permits you to buy 1 dollar for 120 yen). The option has 1 year to expiration and the exchange rate volatility is 10%. Let n = 3.
a. What is the price of a European call? An American call?
b. What is the price of a European put? An American put?
c. How do you account for the pattern of early exercise across the two options?