Sppose the sampp 500 futures price is 1000 30 r 5 5 t

Question

Suppose the S&P 500 futures price is 1000, = 30%; r = 5%; = 5%; T = 1, and n = 3 (n refers to the number of binomial periods).

[Explicit steps of calculation is required]

(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?