Suppose the S&P 500 futures price is 1000, = 30%, r = 5%, = 5%,

Question:

Suppose the S&P 500 futures price is 1000, σ = 30%, r = 5%, δ = 5%, T = 1, and n = 3.
a. What are the prices of European calls and puts for K = $1000? Why do you find the prices to be equal?
b. What are the prices of American calls and puts for K = $1000?
c. What are the time-0 replicating portfolios for the European call and put?