1 a) Let S = $100, K = $95, r = 8%, T = 1, and = 0. Let u = 1.3, d = 0.8, and n = 2 (n refers to the number of binomial periods). Construct the binomial tree for an American put option. At each node provide the premium, , and B. (In other words, construct a complete binomial tree for the option.)

b)Let

S = $40, K = $40, r = 8% (continuously compounding), = 30%, = 0, T = 0.5

year and n = 2 (n refers to the number of binomial periods).

(i)

Construct the binomial tree for the stock. What are u and d?

(ii)

Show that the call price is $4.110.

(iii)

Compute the prices of American and European puts.