The price of a stock share (no dividend, current price is 50) follows a GBM with drift 12% and volatility 35%; the continuously compounded risk free rate is 5%. Consider a (European-style) lookback call with floating strike, whose payoff is (Smax -Smin). Find the option price, by approximating the underlying stochastic process by a three-step binomial tree (the option matures in nine months, and each time step is three months).