Finance, Economics, and Mathematics

Chapter 9The Heath, Jarrow, Morton Model

Written in 1994; printed in Economic Notes, 36 (3) (2008), 205–207.

The price at time τ of a discount bond maturing at T is subject to the dynamics

with

where is the market price of risk (see Vasicek, 1977, Chapter 6 of this volume). This can be written as

1

where

Integrate Eq. (1) with respect to τ from 0 to t,

and differentiate with respect to T. This produces

2

where σ_F is the volatility of the forward rates and

Eq. (2) is the Heath, Jarrow, Morton (1992) model.

If are vectors, their products are interpreted as inner products.

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