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Option Pricing Using The Term Structure Of Interest Rates To Hedge Systematic Discontinuities In Asset Returns

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  • Robert Jarrow
  • Dilip Madan

Abstract

This paper demonstrates the use of term-structure-related securities in the design of dynamic portfolio management strategies that hedge certain systematic jump risks in asset return. Option pricing formulas based on the absence of arbitrage opportunities in this context are also developed. the analysis is for the case where assets returns are driven by a finite number of Brownian motions and an "m"-variate point process. the inclusion of :the additional traded assets in the term structure makes it possible to hedge systematic jumps imbedded in the "m" variate point process. Copyright 1995 Blackwell Publishers.

Suggested Citation

  • Robert Jarrow & Dilip Madan, 1995. "Option Pricing Using The Term Structure Of Interest Rates To Hedge Systematic Discontinuities In Asset Returns," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 311-336.
  • Handle: RePEc:bla:mathfi:v:5:y:1995:i:4:p:311-336
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    Citations

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    Cited by:

    1. Dilip Madan & Haluk Unal, 1996. "Pricing the Risks of Default," Center for Financial Institutions Working Papers 94-16, Wharton School Center for Financial Institutions, University of Pennsylvania.
    2. Bossaerts, P. & Ghysels, E. & Gourieroux, C., 1996. "Arbitrage-Based Pricing when Volatility is Stochastic," Cahiers de recherche 9615, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. John Crosby, 2008. "A multi-factor jump-diffusion model for commodities," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 181-200.
    4. Sanjiv Ranjan Das, 1997. "An Efficient Generalized Discrete-Time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model," NBER Technical Working Papers 0212, National Bureau of Economic Research, Inc.
    5. Consigli, Giorgio, 2002. "Tail estimation and mean-VaR portfolio selection in markets subject to financial instability," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1355-1382, July.
    6. Jarrow, Robert A. & Turnbull, Stuart M., 2000. "The intersection of market and credit risk," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 271-299, January.
    7. Giannetti, Antoine & Clark, John M. & Anderson, Randy I., 2004. "Model risk and option hedging," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(5), pages 659-677, December.
    8. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
    9. repec:wsi:ijtafx:v:18:y:2015:i:04:n:s0219024915500247 is not listed on IDEAS
    10. Koichi Matsumoto, 2003. "Implied Default Probability and Credit Derivatives," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 10(2), pages 129-149, September.
    11. Liu, Sheen & Shi, Jian & Wang, Junbo & Wu, Chunchi, 2009. "The determinants of corporate bond yields," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(1), pages 85-109, February.
    12. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    13. Karl Friedrich Mina & Gerald H. L. Cheang & Carl Chiarella, 2015. "Approximate Hedging Of Options Under Jump-Diffusion Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-26.
    14. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
    15. C. Mancini, 2002. "The European options hedge perfectly in a Poisson-Gaussian stock market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 87-102.
    16. Guan, Lim Kian & Ting, Christopher & Warachka, Mitch, 2005. "The implied jump risk of LIBOR rates," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2503-2522, October.
    17. Mauricio Junca & Rafael Serrano, 2014. "Utility maximization in pure-jump models driven by marked point processes and nonlinear wealth dynamics," Papers 1411.1103, arXiv.org, revised Sep 2015.
    18. Gerald H.L. Cheang & Carl Chiarella, 2008. "Hedge Portfolios in Markets with Price Discontinuities," Research Paper Series 218, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Yao, Yong, 1999. "Term structure modeling and asymptotic long rate," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 327-336, December.
    20. A. Craig Burnside & Jeremy J. Graveline, 2012. "On the Asset Market View of Exchange Rates," NBER Working Papers 18646, National Bureau of Economic Research, Inc.
    21. Jiri Hoogland & Dimitri Neumann & Michel Vellekoop, 2002. "Symmetries in Jump-Diffusion Models with Applications in Option Pricing and Credit Risk," Finance 0203001, EconWPA.
    22. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    23. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    24. Steven Kou, 2000. "A Jump Diffusion Model for Option Pricing with Three Properties: Leptokurtic Feature, Volatility Smile, and Analytical Tractability," Econometric Society World Congress 2000 Contributed Papers 0062, Econometric Society.
    25. Björk, T. & Kabanov, Y. & Runggaldier, W., 1995. "Bond markets where prices are driven by a general marked point process," SSE/EFI Working Paper Series in Economics and Finance 88, Stockholm School of Economics.

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