The following tree depicts the price evolution of a stock. Each sub-period is six months and the entire period is therefore 12 months. The annual interest rate (continuous compounding) is 2.5%.

1. 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 European put with an exercise price of $73.

B. Use the three ending prices and todays price to calculate the return volatility. The following hints may be useful to you. First, calculate the three percentage returns (e.g., 119/70 1 = 0.7). Then, use the three returns to calculate the standard deviation or volatility according to the standard statistical formula: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 $70) and value the same European put in Part A. Compare the two values.

$119.00 90.00 $70.00 $71.05 $60.00 - $56.00 '-; -5) i=1 $119.00 90.00 $70.00 $71.05 $60.00 - $56.00 '-; -5) i=1