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

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  • Carl Chiarella
  • Christina Sklibosios

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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  • Carl Chiarella & Christina Sklibosios, 2003. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 10(2), pages 87-127, September.
    • Handle: RePEc:kap:apfinm:v:10:y:2003:i:2:p:87-127
    DOI: 10.1007/s10690-005-6006-0
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    10. Robert A. Jarrow & Arkadev Chatterjea, 2019. "Interest Rates," World Scientific Book Chapters, in: An Introduction to Derivative Securities, Financial Markets, and Risk Management, chapter 2, pages 22-52, World Scientific Publishing Co. Pte. Ltd..
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    12. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899, November.
    13. Carl Chiarella & Thuy‐Duong Tô, 2003. "The jump component of the volatility structure of interest rate futures markets: An international comparison," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(12), pages 1125-1158, December.
    14. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    15. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson‐Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94, October.
    16. 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.
    17. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    18. George Chacko, 2002. "Pricing Interest Rate Derivatives: A General Approach," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 195-241, March.
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    Cited by:

    1. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2010. "Real-world jump-diffusion term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 23-37.
    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;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 299-313, December.
    3. Wang, Shin-Yun & Lin, Shih-Kuei, 2010. "The pricing and hedging of structured notes with systematic jump risk: An analysis of the USD knock-out reversed swap," International Review of Economics & Finance, Elsevier, vol. 19(1), pages 106-118, January.
    4. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlögl, 2007. "A Markovian Defaultable Term Structure Model With State Dependent Volatilities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 155-202.
    5. 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.
    6. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlogl, 2007. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 365-399.
    7. Carl Chiarella & Thuy-Duong Tô, 2006. "The Multifactor Nature of the Volatility of Futures Markets," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 163-183, May.
    8. Bruti-Liberati Nicola & Nikitopoulos-Sklibosios Christina & Platen Eckhard, 2006. "First Order Strong Approximations of Jump Diffusions," Monte Carlo Methods and Applications, De Gruyter, vol. 12(3), pages 191-209, October.
    9. Son-Nan Chen & Pao-Peng Hsu & Chang-Yi Li, 2016. "Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 573-592, April.
    10. 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.
    11. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    12. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    14. 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.

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