3. Suppose at time t 5 0, we are given prices for four zero-coupon bonds (B1, B2, B3, B4) that mature at times t 5 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 5 0 on a loan that begins at time t 5 i and ends at time t 5 i 1 1. In other words, if a borrower borrows N GBP at time i, he or she will pay back N(1 1 fi) GBP at time t 5 i 1 1.

The spot rates are denoted by ri. By definition, we have r 5 f0 (6.43)

The {Bi} and all forward loans are default-free, so that there is no credit risk. You are given the following live quotes:

B1 5 0:92=0:94; B2 5 0:85=0:88; B3 5 0:82=0:85 (6.44)

and f0 5 8:10=8:12; f1 5 9:01=9:03; f2 5 10:12=10:16; f3 5 18:04=18:10 (6.45)

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?