Problem 3: Consider the binomial model for the interest rate model where

r₀ = 0.25 and

r_n+1 := (1 + r_n)_n+1 1.

Here the iid random variables _n take values u := 2 and d := 0.5 with one- period risk-neutral probabilities p = 0.75 and q = 0.25.

Determine the fair swap rate R for a contract with N := 2 payments at times 1, ..., N. Recall that there is no cost of entry into the swap and that at times n = 1, ..., N one side pays the fixed interest R, while the other side pays the floating interest rate r_n1.