Article1994

A MULTIFACTOR GAUSS MARKOV IMPLEMENTATION OF HEATH, JARROW, AND MORTON

250 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

Abstract

Working within the Heath‐Jarrow‐Morton framework and using the theory of stochastic equations in infinite dimensions, a useful multifactor Gauss‐Markov model for the movement of the whole of the yield curve is derived. Swaptions are priced. They are hedged by eliminating random terms between the semimartingale representations of the swaption and hedging instruments. Hedging efficiency is analyzed. the model is fitted to the swap/cap strips in Australia. Computation times on a 20‐MHz laptop computer are acceptable.

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References

1985A Theory of the Term Structure of Interest Rates 1992Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation 1990Pricing Interest-Rate-Derivative Securities 1986Term Structure Movements and Pricing Interest Rate Contingent Claims 1992Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model 1989An Exact Bond Option Formula 1991Bond and Option Pricing when Short Rates are Lognormal

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2001The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks 2001Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model 2003Optimal consumption and investment strategies with stochastic interest rates 1999The Dynamics of the Forward Interest Rate Curve: A Formulation with State Variables 2002On the construction of finite dimensional realizations for nonlinear forward rate models 2003The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions

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