Note: This abstract was revised by the author since June 1997.Forward rate dynamics are modeled as a random field. In contrast to multi-factor models, random field models offer a parsimonious description of term structure dynamics, while eliminating the self-inconsistent practice of recalibration. The form of the drift of the instantaneous forward rate process necessary to preclude arbitrage under the risk neutral measure is obtained. Forward measures are characterized, and used to price a bond option when the forward volatility structure depends upon the square root of the current spot rate. In addition, it is demonstrated that random field models offer a parsimonious method to account for parameter uncertainty, inherently predicting that the best hedging instrument for a given asset is one of similar maturity. Finally, a random field is shown to be supported within a general equilibrium framework, allowing the risk-neutral measure and risk premia to be identified.

Modeling the Term Structure of Interest Rates provides a comprehensive review of the continuous-time modeling techniques of the term structure applicable to value and hedge default-free bonds and other interest rate derivatives.

This book offers a new approach to interest rate and modeling term structure by using models based on optimization of dynamical systems, rather than the traditional stochastic differential equation models. The authors use dynamic models to estimate the term structure of interest rates and show the reader how to build their own numerical simulations. It includes software that will enable readers to simulate the various models covered in the book.