A. Volatility is an important input in option valuation, but it is not an observed variable and must be estimated. It can be estimated using historical data. Alternatively, since option prices can be observed, we can use the observed option price together with other market data to imply volatility. This volatility can then be used to value other options. Suppose an American put option written on the CAD/ exchange rate with an exercise price of $0.012/ and a time-to-maturity of nine months is currently trading at $0.767810³. The Canadian interest rate is 2.75% and the Japanese interest rate is 0.5%, both compounded continuously. The current exchange rate is $0.0122/. Use a three-step tree to imply the volatility (assume that the contract is for 1,000, i.e., multiply the current FX rate, the exercise price, and the option value by 1,000). (Hint: set up the tree in a spreadsheet and find the implied volatility by Solver.)

B. In the same set-up as above, suppose everything remains the same except that someone has already estimated the volatility to be 20%, and the American put for 1,000 is worth $0.7174. What is the implied interest rate in Japan?