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Finance, Economics, and Mathematics by Robert C. Merton, Oldrich A. Vasicek

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Chapter 9The Heath, Jarrow, Morton Model

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

The price c09-math-0001 at time τ of a discount bond maturing at T is subject to the dynamics

equation

with

equation

where c09-math-0004 is the market price of risk (see Vasicek, 1977, Chapter 6 of this volume). This can be written as

1 equation

where

equation

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

equation

and differentiate with respect to T. This produces

2 equation

where σF is the volatility of the forward rates and

equation

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

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

References ...

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