The following tree depicts the price evolution of a stock. Each sub-period is nine months and the entire period is therefore 18 months. The annual interest rate (continuous compounding) is 3.5%. A. Use the simple binomial tree method (i.e., form a risk-neutral portfolio to find the optimal combination at each node as we did in class) to find the value of an American call with an exercise price of $12.5. B. Use the three ending prices and today's price to calculate the return volatility. The following hints may be useful to you. First, calculate the three percentage returns (e.g., 15/13.35-1 =0.1235955). Then, annualize the return if necessary (e.g., 0.1235955(12/18)=0.082397). Finally, use the three annualized returns to calculate the standard deviation or volatility according to the standard statistical formula: 2=n11i=1n(rir)2 where n is the number of observations ( 3 in our case) and r_bar is the mean which is the simple average of the three returns in our case. Please keep six decimal places in calculations. C. Use the volatility obtained from Part B and the formulas for u,d and p to build a binomial tree (based on the current stock price of \$13.35) and value the same option in Part A. Compare the two values