There are a lot of options more complicated than the call or put options we have covered in class. One example is the Lookback Option, which has a payoff given by the maximum or minimum value that the underlying asset reaches in a given period (from now to the maturity of the option). Consider a European lookback option to sell a stock 2 years from now for the maximum price of the stock during the coming 2 years. This option allows one to time the market perfectly and get the most from selling the stock. Suppose that the current price of the stock is $100. It does not pay dividends, and each year it can go up by 25% or down by 20%. The annual risk free rate is 5%. The figure below shows the evolution of the stock price: Find the value of this option.