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

Published online by Cambridge University Press:  06 April 2009

Koji Inui  and
Masaaki Kijima
Koji Inui
Affiliation:
Financial Research Department, NLI Research Institute, 1–1–1 Yuraku-cho, Chiyoda-ku, Tokyo 100–0006, Japan
Masaaki Kijima
Affiliation:
Faculty of Economics, Tokyo Metropolitan University, 1–1 Minami-Ohsawa, Hachiohji, Tokyo 192–0397, Japan.
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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).

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 33 , Issue 3 , September 1998 , pp. 423 - 440
Copyright
Copyright © School of Business Administration, University of Washington 1998

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References

Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–654.Google Scholar
Bliss, R. R., and Ritchken, P.. “Empirical Tests of Two State-Variable HJM Models.” Working Paper 95–13, Federal Reserve Bank of Atlanta (1995).Google Scholar
Carverhill, A. “When is the Spot Rate Markovian?” Mathematical Finance, 4 (1994), 305–312.Google Scholar
Chan, K. C.; Karolyi, G. A.; Longstaff, F. A.; and Sanders, A. B.. “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate.” Journal of Finance, 47 (1992), 1209–1227.Google Scholar
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (1985), 385–407.Google Scholar
Flesaker, B. “Testing the Heath-Jarrow-Morton/Ho-Lee Model of Interest Rate Contingent Claims Pricing.” Journal of Financial and Quantitative Analysis, 28 (1993), 483–495.Google Scholar
Heath, D.; Jarrow, R.; and Morton, A.. “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.” Econometrica, 60 (1992), 77–105.Google Scholar
Ho, T. S., and Lee, S.. “Term Structure Movements and Pricing Interest Rate Contingent Claims.” Journal of Finance, 41 (1986), 1011–1028.CrossRefGoogle Scholar
Hull, J., and White, A.. “Pricing Interest-Rate-Derivative Securities.” Review of Financial Studies, 3 (1990), 573–592.Google Scholar
Hull, J., and White, A.. “Bond Option Pricing Based on a Model for the Evolution of Bond Prices.” Advances in Futures Options Research, 6 (1993), 1–13.Google Scholar
Jamshidian, F. “Bond and Option Evaluation in the Gaussian Interest Rate Model.” Research in Finance, 9 (1991), 131–170.Google Scholar
Jeffrey, A. “Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics.” Journal of Financial and Quantitative Analysis, 30 (1995), 619–642.Google Scholar
Karatzas, I., and Shreve, S. E.. Brownian Motion and Stochastic Calculus. New York, NY: Springer (1988).Google Scholar
Karlin, S., and Taylor, H.. A Second Course in Stochastic Processes. New York, NY: Academic Press (1981).Google Scholar
Kijima, M., and Nagayama, I.. “Efficient Numerical Procedures for the Hull-White Extended Vasicek Model.” Journal of Financial Engineering, 3 (1994), 275–292.Google Scholar
Kijima, M., and Nagayama, I.. “A Numerical Procedure for the General One-Factor Interest Rate Model.” Journal of Financial Engineering, 5 (1996), 317–337.Google Scholar
Kijima, M., and Yoshida, T.. “A Simple Option Pricing Model with Markovian Volatilities.” Journal of the Operations Research Society of Japan, 36 (1993), 149–166.Google Scholar
Langetieg, T. C. “A Multivariate Model of the Term Structure.” Journal of Finance, 35 (1980), 71–97.Google Scholar
Longstaff, F. A., and Schwartz, E. S.. “Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model.” Journal of Finance, 47 (1992), 1259–1282.Google Scholar
Ritchken, P., and Sankarasubramanian, L.. “Volatility Structures of Forward Rates and the Dynamics of the Term Structure.” Mathematical Finance, 5 (1995), 55–72.Google Scholar