Articlegreen1998

A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models

164 citations0/0 files storedJournal of Financial and Quantitative Analysis

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

We consider the general n-factor Heath, Jarrow, and Morton model (1992) and provide a sufficient condition on the volatility structure for the spot rate process to be Markovian with 2n state variables. The price of a discount bond is also Markovian with the same state variables and, hence, claims against the term structure can be efficiently priced using standard simulation techniques. Our results extend earlier works such as Ritchken and Sankarasubramanian (1995) where the one-factor model is treated, and Carverhill (1994), where the volatility structure is non-random. Numerical experiments show that our model can explain the volatility smile observed in the interest rate options market and also overcome the biases noted by Flesaker (1993).

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References

1973The Pricing of Options and Corporate Liabilities 1985A Theory of the Term Structure of Interest Rates 2007Brownian Motion and Stochastic Calculus 1992Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation 1990Pricing Interest-Rate-Derivative Securities 1992An Empirical Comparison of Alternative Models of the Short-Term Interest Rate 1986Term Structure Movements and Pricing Interest Rate Contingent Claims 1992Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model

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2000The Term Structure of Interest Rates as a Random Field 2001Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model 2008A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives 2002On the construction of finite dimensional realizations for nonlinear forward rate models 2010Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

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