4. Suppose at time t = 0, we are given prices for four zero-coupon bonds (B1, B2, B3, B4) that mature at times t = 1, 2, 3, and 4. This forms the term structure of interest rates. We also have the one-period forward rates (f0, f1, f2, f3), where each fi is the rate contracted at time t = 0 on a loan that begins at time t = i and ends at time t = i + 1. In other words, if a borrower borrows N GBP at time i, he or she will pay back N(1 + fi) GBP at time t = i + 1. The spot rates are denoted by ri. By definition we have r = f0 (71) The {Bi} and all forward loans are default-free, so that there is no credit risk. You are given the following live quotes: B1 = .92/.94, B2 = .85/.88, B3 = .82/.85 (72) and f0 = 8.10/8.12, f1 = 9.01/9.03, f2 = 10.12/10.16, f3 = 18.04/18.10 (73)

(a) Given the data on forward rates, obtain arbitrage-free prices for the zero-coupon bonds, B1 and B2.

(b) What is the three-period swap rate under these conditions?