Problem 2. [20 points] We have shown that any derivative security C of a stock S has a value that can be calculated as the expected discounted value of its payoff in the risk-neutral q-measure. Consider a 3-month European call option on the arithmetic historical average price at expiration of a stock S that pays no dividends and evolves according to a 3-period binomial tree. The stock evolves as follows. In each period the stock price goes up by a factor of 1.3 or down by a factor of 1/(1.3). Each period is 1/12 of a year long, and the riskless interest rate is 8% per year continuously compounded. Use risk-neutral valuation to find the value of a call where the initial stock price is $100 and the payoff at expiration is max [Savg (T) 100, 0], where Savg(T) at expiration, along any path the stock takes, is the arithmetic historical average price of the stock along that path, i.e. the average price at the four nodes along the three monthly steps it took, starting with 100 and ending with the final price. Save(T)