1. You observe the following default-free discount bond prices B(t, Ti), where time is measured in years: B(0, 1) = 95, B(0, 2) = 93, B(0, 3) = 91, B(0, 4) = 89 (150) These prices are assumed to be arbitrage-free. In addition, you are given the following cap-floor volatilities: σ(0, 1) = .20, σ(0, 2) = .25, σ(0, 3) = .20, σ(0, 4) = .18 (151) where σ(t, Ti) is the (constant) volatility of the Libor rate LTi that will be observed at Ti with tenor of 1 year.

(a) Using the Black-Derman-Toy model, calibrate a binomial tree to these data.

(b) Suppose you are given a bond call option with the following characteristics. The underlying, B(2, 4), is a two-period bond, expiration T = 2, strike KB = 93. You know that the BDT tree is a good approximation to arbitrage-free Libor dynamics. What is the forward price of B(2, 4)?

(c) Calculate the arbitrage-free value of this call option using the BDT approach.