Consider a binomial model with a corporate bond B and a credit default swap CDS. B pays off one in state u and zero in state d and costs B0 today. CDS pays off zero in state u and one in state d and costs CDS0 today.

a) Writedownanexpressionfortherisk-freerateforthistree.

b) Consider a general derivative that pays off Xu in state u and Xd in state d. Write down a general expression for the price X0 of the derivative today. Your answer should depend on only B0, CDS0, Xu, and Xd.

Hint: Proceed exactly as: Construct a replicating portfolio with 1 corporate bonds and 2 credit default swaps that matches the payoff of X both in state u and in state d.