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Preferences, Levy Jumps and Option Pricing

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  • Chenghu Ma

Abstract

This paper derives an equilibrium formula for pricing European options and other contingent claims which allows incorporating impacts of several important economic variable on security prices including, among others, representative agent preferences, future volatility and rare jump events. The derived formulae is general and flexible enough to include some important option pricing formulae in the literature, such as Black-Scholes, Naik-Lee, Cox-Ross and Merton option pricing formulae. The existence of jump risk as a potential explanation of the moneyness biases associated with the Black-Scholes model is explored.

Suggested Citation

  • Chenghu Ma, 2013. "Preferences, Levy Jumps and Option Pricing," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    • Handle: RePEc:wyi:wpaper:001995
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    File URL: https://econpub.xmu.edu.cn/research/repec/upload/200711151442517055475115776.pdf
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    References listed on IDEAS

    as
    1. Ma, Chenghu, 2000. "An existence theorem of intertemporal recursive utility in the presence of Levy jumps," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 509-526, December.
    2. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    3. Jarrow, Robert A & Rosenfeld, Eric R, 1984. "Jump Risks and the Intertemporal Capital Asset Pricing Model," The Journal of Business, University of Chicago Press, vol. 57(3), pages 337-351, July.
    4. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    5. Brown, Stephen J & Dybvig, Philip H, 1986. "The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 41(3), pages 617-630, July.
    6. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 317-317.
    7. Chenghu Ma, 1998. "A Discrete‐Time Intertemporal Asset Pricing Model: GE Approach with Recursive Utility," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 249-275, July.
    8. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    9. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    10. Ma, Chenghu, 2006. "Intertemporal recursive utility and an equilibrium asset pricing model in the presence of Levy jumps," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 131-160, April.
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    Keywords

    equilibrium option pricing; recursive utility; Levy jumps.;
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