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The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach

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Author Info
Carl Chiarella () (School of Finance and Economics, University of Technology, Sydney)
Hing Hung
Thuy-Duong To (School of Banking and Finance, University of NSW)

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Abstract

This paper considers the dynamics for interest rate processes within a multi-factor Heath, Jarrow and Morton (1992) specification. Despite the flexibility of and the notable advances in theoretical research about the HJM models, the number of empirical studies is still inadequate. This paucity is principally because of the difficulties in estimating models in this class, which are not only high-dimensional, but also nonlinear and involve latent state variables. This paper treats the estimation of a fairly broad class of HJM models as a nonlinear filtering problem, and adopts the local linearization filter of Jimenez and Ozaki (2003), which is known to have some desirable statistical and numerical features, to estimate the model via the maximum likelihood method. The estimator is then applied to the interbank offered-rates of the U.S, U.K, Australian and Japanese markets. The two-factor model, with the factors being the level and the slope effect, is found to be a reasonable choice for all of the markets. However, the contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims differ considerably from one market to another.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 151.

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Length: 30
Date of creation: 01 Jan 2005
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Handle: RePEc:uts:rpaper:151

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Related research
Keywords: term structure; Heath-Jarrow-Morton; local linearization; filtering;

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Find related papers by JEL classification:
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Jegadeesh, Narasimhan & Pennacchi, George G, 1996. "The Behavior of Interest Rates Implied by the Term Structure of Eurodollar Futures," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(3), pages 426-46, August. [Downloadable!] (restricted)
  2. To, Thuy Duong & Carl Chiarella, 2003. "The Jump Component of the Volatility Structure of Interest Rate Futures Markets: An International Comparison," Royal Economic Society Annual Conference 2003 205, Royal Economic Society. [Downloadable!]
  3. Ram Bhar & Carl Chiarella, 1995. "Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
  4. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
  5. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January. [Downloadable!] (restricted)
  6. Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May. [Downloadable!] (restricted)
  7. Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257. [Downloadable!] (restricted)
    Other versions:
  8. Ram Bhar & Carl Chiarella & Hing Hung & Wolfgang Runggaldier, 2004. "The Volatility of the Instantaneous Spot Interest Rate Implied by Arbitrage Pricing - A Dynamic Bayesian Approach," Finance 0409002, EconWPA. [Downloadable!]
  9. Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April. [Downloadable!] (restricted)
  10. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 12(4), pages 687-720.
  11. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
  12. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
    Other versions:
  13. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March. [Downloadable!] (restricted)
  14. Moraleda, Juan M. & Vorst, Ton C. F., 1997. "Pricing American interest rate claims with humped volatility models," Journal of Banking & Finance, Elsevier, vol. 21(8), pages 1131-1157, August. [Downloadable!] (restricted)
  15. Narasimhan Jegadeesh & George G. Pennacchi, 1996. "The behavior of interest rates implied by the term structure of Eurodollar future," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 426-451.
  16. Knez, Peter J & Litterman, Robert & Scheinkman, Jose Alexandre, 1994. " Explorations into Factors Explaining Money Market Returns," Journal of Finance, American Finance Association, vol. 49(5), pages 1861-82, December. [Downloadable!] (restricted)
  17. Pagan, A.R. & Hall, A.D. & Martin, V., 1995. "Modelling the Term Structure," Papers 284, Australian National University - Department of Economics.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena. [Downloadable!]
  2. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer, vol. 12(2), pages 109-141, June. [Downloadable!] (restricted)
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