Consider a binomial model with two securities, 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) Write down an expression for the risk-free rate for this tree.

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 in question 1.: 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.