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A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework

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Author Info
Carl Chiarella ()
Christina Sklibosios

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Abstract

This paper considers a class of term structure models that is a parameterisation of the Shirakawa (1991) extension of the Heath et al. (1992) model to the case of jump-diffusions. We consider specific forward rate volatility structures that incorporate state dependent Wiener volatility functions and time dependent Poisson volatility functions. Within this framework, we discuss the Markovianisation issue, and obtain the corresponding affine term structure of interest rates. As a result we are able to obtain a broad tractable class of jump-diffusion term structure models. We relate our approach to the existing class of jump-diffusion term structure models whose starting point is a jump-diffusion process for the spot rate. In particular we obtain natural jump-diffusion versions of the Hull and White (1990, 1994) one-factor and two-factor models and the Ritchken and Sankarasubramanian (1995) model within the HJM framework. We also give some numerical simulations to gauge the effect of the jump-component on yield curves and the implications of various volatility specifications for the spot rate distribution. Copyright Springer Science + Business Media, Inc. 2003

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File URL: http://hdl.handle.net/10.1007/s10690-005-6006-0
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Publisher Info
Article provided by Springer in its journal Asia-Pacific Financial Markets.

Volume (Year): 10 (2003)
Issue (Month): 2 (September)
Pages: 87-127
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Handle: RePEc:kap:apfinm:v:10:y:2003:i:2:p:87-127

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Web page: http://springerlink.metapress.com/link.asp?id=102851

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Related research
Keywords: jump-diffusions; Markovian HJM model; state dependent volatility;

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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. Carl Chiarella & Nadima El-Hassan, 1996. "A Preference Free Partial Differential Equation for the Term Stucture of Interest Rates," Working Paper Series 63, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
  2. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 423-440, September. [Downloadable!]
  3. 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!]
  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. 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!]
  6. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January. [Downloadable!] (restricted)
  7. 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)
  8. Björk, Tomas & Gombani, Andrea, 1997. "Minimal Realizations of Forward Rates," Working Paper Series in Economics and Finance 182, Stockholm School of Economics. [Downloadable!]
  9. Carl Chiarella & Oh-Kang Kwon, 1999. "Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model," Research Paper Series 5, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  10. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 573-92. [Downloadable!] (restricted)
  11. George Chacko, 2002. "Pricing Interest Rate Derivatives: A General Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 15(1), pages 195-241, March.
  12. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Blackwell Publishing, vol. 13(3), pages 383-410. [Downloadable!] (restricted)
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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. Carl Chiarella & Thuy-Duong Tô, 2006. "The Multifactor Nature of the Volatility of Futures Markets," Computational Economics, Springer, vol. 27(2), pages 163-183, May. [Downloadable!] (restricted)
  2. Jirô Akahori & Takahiro Tsuchiya, 2006. "What is the Natural Scale for a Lévy Process in Modelling Term Structure of Interest Rates?," Asia-Pacific Financial Markets, Springer, vol. 13(4), pages 299-313, December. [Downloadable!] (restricted)
    Other versions:
  3. Nicola Bruti-Liberati & Eckhard Platen, 2005. "On the Strong Approximation of Jump-Diffusion Processes," Research Paper Series 157, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  4. Carl Chiarella & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2005. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton with Jumps," Research Paper Series 167, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  5. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2007. "Pricing under the Real-World Probability Measure for Jump-Diffusion Term Structure Models," Research Paper Series 198, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  6. Carl Chiarella & Erik Schlögl & Christina Nikitopoulos-Sklibosios, 2004. "A Markovian Defaultable Term Structure Model with State Dependent Volatilities," Research Paper Series 135, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
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