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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
Chiarella, Carl
Hung, Hing
T, Thuy-Duong

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Abstract

The dynamics for interest rate processes within the well-known multi-factor Heath, Jarrow and Morton (HJM) specification are considered. Despite the flexibility of and the notable advances in theoretical research about the HJM model, the number of empirical studies of it is still very sparse. This paucity is principally due to the difficulties in estimating models in this class, which are not only high-dimensional, but also nonlinear and involve latent state variables. The estimation of a fairly broad class of HJM models as a nonlinear filtering problem is undertaken by adopting the local linearization filter, which is known to have some desirable statistical and numerical features, so enabling the estimation of the model via the maximum likelihood method. The estimator is then applied to the US, the UK and the Australian markets. Different two- and three-factor models are found to be the best for each market, with the factors being the level, the slope and the "twist" effect. The contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims are found to differ considerably from one market to another.

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Publisher Info
Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 53 (2009)
Issue (Month): 6 (April)
Pages: 2075-2088
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Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2075-2088

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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. 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)
  3. 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.
  4. 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!]
  5. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
  6. 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)
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  7. 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!]
  8. 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)
  9. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January. [Downloadable!] (restricted)
  10. 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)
  11. 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)
  12. 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)
  13. 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.
  14. 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)
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  15. 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!]
  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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(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. 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)
  2. 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!]
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