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 call option written on a FX with an exercise price of $1.25/FC (where FC stands for foreign currency) and a time-to-maturity of 18 months is currently trading at $0.2749. The $ interest rate and the foreign interest rates are 1.5% and 5.5% respectively (both continuously compounded). The current FC rate is $1.48/FC. Use a three-step tree to imply the volatility. (Hint: set up the tree in a spreadsheet and find the implied volatility by Solver. When your initial guess is too low, Solver may not be able to find a solution since the option could be optimally exercised. In this case, start with a higher volatility guess.) In the same set-up as above, suppose everything remains the same except that we don't know the foreign interest rate and someone has already estimated the volatility to be 40%, and the American call is worth $0.33. What is the implied foreign interest rate? (Hint: to ensure better convergence, set the Solver objective function as, e.g., (COCT)2106 and try to make it zero, where CO and CT are respectively the observed and tree values of the options.)