The Mathematics of Financial Modelingand Investment Management

20-Term Structure Page 609 Wednesday, February 4, 2004 1:33 PM

Term Structure Modeling and Valuation of Bonds and Bond Options 609

EXHIBIT 20.2 Short-Term Forward Rates

Notation Forward Rate

1 f 0 3.00

1 f 1 3.60

1 f 2 3.92

1 f 3 5.15

1 f 4 6.54

1 f 5 6.33

1 f 6 6.23

1 f 7 5.79

1 f 8 6.01

1 f 9 6.24

1 f 10 6.48

1 f 11 6.72

1 f 12 6.97

1 f 13 6.36

1 f 14 6.49

1 f 15 6.62

1 f 16 6.76

1 f 17 8.10

1 f 18 8.40

1 f 19 8.72

from observed swap rates in the interest rate swap market. In a generic

interest rate swap two parties agree to exchange cash flows based on a

notional amount where (1) one party pays a fixed rate and receives a

floating rate and (2) the other party agrees to pay a floating rate and

receives a fixed rate. The fixed rate is called the swap rate. A swap curve

can be constructed that is unique to a country where there is a swap

market for converting fixed cash flows to floating cash flows in that

country’s currency.

Typically, the reference rate for the floating rate is 3-month LIBOR.

Effectively, the swap curve indicates the fixed rate (i.e., swap rate) that a

party must pay to lock in 3-month LIBOR for a specified future period.

By locking in 3-month LIBOR it is meant that a party that pays the

floating rate (i.e., agrees to pay 3-month LIBOR) is locking in a borrow-

ing rate; the party receiving the floating rate is locking in an amount to

be received. Because 3-month LIBOR is being exchanged, the swap

curve is also called the LIBOR curve.