Use a three-time-step tree to value an American floating lookback call option on a currency when the initial exchange rate is 1.6 , the domestic risk-free rate is $5 \%$ per annum, the foreign risk-free interest rate is $8 \%$ per annum, the exchange rate volatility is $15 \%$, and the time to maturity is 18 months. Use the approach in Section 27.5.