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

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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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  • Carl Chiarella & Hing Hung & Thuy-Duong To, 2005. "The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach," Research Paper Series 151, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:151
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    Cited by:

    1. Antje Berndt & Peter Ritchken & Zhiqiang Sun, 2010. "On Correlation and Default Clustering in Credit Markets," Review of Financial Studies, Society for Financial Studies, vol. 23(7), pages 2680-2729, July.
    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;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    3. 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.
    4. Giuliano De Rossi, 2004. "Maximum likelihood estimation of the Cox-Ingersoll-Ross model using particle filters," Computing in Economics and Finance 2004 302, Society for Computational Economics.
    5. Baaquie, Belal E. & Pan, Tang, 2011. "Simulation of coupon bond European and barrier options in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 263-289.
    6. Robert J. Elliott & John W. Lau & Hong Miao & Tak Kuen Siu, 2012. "Viterbi-Based Estimation for Markov Switching GARCH Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(3), pages 219-231, August.
    7. J. C. Jimenez & T. Ozaki, 2006. "An Approximate Innovation Method For The Estimation Of Diffusion Processes From Discrete Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 77-97, January.
    8. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.

    More about this item

    Keywords

    term structure; Heath-Jarrow-Morton; local linearization; filtering;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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