3. Suppose that S = $100, K = $100, r = 0.08, = 0.30, =...

3. Suppose that S = $100, K = $100, r = 0.08, σ = 0.30, δ = 0, and T = 1. Construct a standard two-period binomial stock price tree.

a. Consider stock price averages computed by averaging the 6-month and 1-year prices. What are the possible arithmetic and geometric averages after 1 year?

b. Construct a binomial tree for the average. How many nodes does it have after 1 year? (Hint: While the moves ud and du give the same year-1 price, they do not give the same average in year 1.)

c. What is the price of an Asian arithmetic average price call?

d. What is the price of an Asian geometric average price call?