Options, Futures, and Other Derivatives, Ninth Edition

Chapter 32 HJM, LMM, and Multiple Zero Curves

The interest rate models discussed in Chapter 31 are widely used for pricing instruments when the simpler models in Chapter 29 are inappropriate. They are easy to implement and, if used carefully, can ensure that most nonstandard interest rate derivatives are priced consistently with actively traded instruments such as interest rate caps, European swap options, and European bond options. Two limitations of the models are:

1. Most involve only one factor (i.e., one source of uncertainty).

2. They do not give the user complete freedom in choosing the volatility structure.

By making the parameters a and σ functions of time, an analyst can use the models so that they fit the volatilities observed in ...