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The reduction of forward rate dependent volatility HJM models to Markovian form: pricing European bond options

Author

Listed:
  • Ramaprasad Bhar
  • Carl Chiarella
  • Nadima El-Hassan
  • and Xiaosu Zheng

Abstract

ABSTRACT The authors consider a single-factor Heath-Jarrow-Morton model with a forward rate volatility function depending upon a function of time to maturity, the instantaneous spot rate of interest, and a forward rate to a fixed maturity. With this specification, the stochastic dynamics determining the prices of interest rate derivatives may be reduced to Markovian form. Furthermore, the evolution of the forward rate curve is completely determined by the two rates specified in the volatility function and it is thus possible to obtain a closed-form expression for bond prices. The prices of bond options are determined by a partial differential equation with two spatial variables. The evaluation of European bond options in this framework using the alternating direction implicit method is discussed.

Suggested Citation

  • Ramaprasad Bhar & Carl Chiarella & Nadima El-Hassan & and Xiaosu Zheng, . "The reduction of forward rate dependent volatility HJM models to Markovian form: pricing European bond options," Journal of Computational Finance, Journal of Computational Finance.
    • Handle: RePEc:rsk:journ0:2160504
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    2. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, April.
    3. Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Chiarella, Carl & Clewlow, Les & Musti, Silvana, 2005. "A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 325-336, March.
    5. Carl Chiarella & Sara Pasquali & Wolfgang J. Runggaldier, 2001. "On Filtering in Markovian Term Structure Models," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 12, pages 139-150, World Scientific Publishing Co. Pte. Ltd..
    6. Y. D'Halluin & P. A. Forsyth & K. R. Vetzal & G. Labahn, 2001. "A numerical PDE approach for pricing callable bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(1), pages 49-77.
    7. Fima Klebaner & Truc Le & Robert Liptser, 2006. "On Estimation of Volatility Surface and Prediction of Future Spot Volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 245-263.
    8. Carl Chiarella & Oh-Kang Kwon, 2000. "A Class of Heath-Jarrow-Morton Term Structure Models with Stochastic Volatility," Research Paper Series 34, Quantitative Finance Research Centre, University of Technology, Sydney.

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