Article1994

WHEN IS THE SHORT RATE MARKOVIAN?

196 citations0/0 files storedMathematical Finance

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

Abstract

We answer this question in the very general context of the n‐factor Heath, Jarrow, and Morton model for the evolution of the term structure of interest rates, with nonrandom volatility. the answer is that a constraint is imposed on the behavior of the volatility structure. We explain the importance of this result for the design of efficient numerical algorithms for the valuation of options on the term structure.

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References

1985A Theory of the Term Structure of Interest Rates 1977An equilibrium characterization of the term structure 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 1990Simple Binomial Processes as Diffusion Approximations in Financial Models 1990Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation 1990Valuing Derivative Securities Using the Explicit Finite Difference Method

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1998A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models 2000The Term Structure of Interest Rates as a Random Field 1995Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics 2003Optimal consumption and investment strategies with stochastic interest rates 1997Transformation of Heath?Jarrow?Morton models to Markovian systems

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