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Pricing Options Under Jump-Diffusion Processes

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  • David S. Bates

Abstract

This paper derives the appropriate characterization of asset market equilibrium when asset prices follow jump-diffusion processes, and develops this general methodology for pricing options on such assets. Specific restrictions on distributions and preferences are imposed, yielding a tractable option pricing model that is valid even when jump risk is systematic and non-diversifiable. The dynamic hedging strategies justifying the option pricing model are described. Comparisons are made throughout the paper to the analogous problem of pricing options under stochastic volatility.

Suggested Citation

  • David S. Bates, "undated". "Pricing Options Under Jump-Diffusion Processes," Rodney L. White Center for Financial Research Working Papers 37-88, Wharton School Rodney L. White Center for Financial Research.
    • Handle: RePEc:fth:pennfi:37-88
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    Cited by:

    1. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    2. Shang-Jin Wei, 1991. "Anticipations of foreign exchange volatility and bid-ask spreads," International Finance Discussion Papers 409, Board of Governors of the Federal Reserve System (U.S.).
    3. David Backus & Mikhail Chernov & Ian Martin, 2011. "Disasters Implied by Equity Index Options," Journal of Finance, American Finance Association, vol. 66(6), pages 1969-2012, December.
    4. van Wijnbergen, Sweder & Olijslagers, Stan & Petersen, Annelie & de Vette, Nander, 2018. "What Option Prices tell us about the ECB's Unconventional Monetary Policies," CEPR Discussion Papers 13371, C.E.P.R. Discussion Papers.
    5. David S. Bates, 2001. "The Market for Crash Risk," NBER Working Papers 8557, National Bureau of Economic Research, Inc.
    6. 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.
    7. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    8. Hilliard, Jimmy E. & Hilliard, Jitka, 2019. "A jump-diffusion model for pricing and hedging with margined options: An application to Brent crude oil contracts," Journal of Banking & Finance, Elsevier, vol. 98(C), pages 137-155.
    9. Mark Broadie & Mikhail Chernov & Michael Johannes, 2009. "Understanding Index Option Returns," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4493-4529, November.
    10. Pedro Santa-Clara & Shu Yan, 2004. "Jump and Volatility Risk and Risk Premia: A New Model and Lessons from S&P 500 Options," NBER Working Papers 10912, National Bureau of Economic Research, Inc.
    11. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2009. "Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options," CIRANO Working Papers 2009s-34, CIRANO.
    12. Lustig, Hanno & Verdelhan, Adrien, 2016. "Does Incomplete Spanning in International Financial Markets Help to Explain Exchange Rates?," Research Papers 3412, Stanford University, Graduate School of Business.
    13. George Skiadopoulos & Stewart Hodges & Les Clewlow, 2000. "The Dynamics of the S&P 500 Implied Volatility Surface," Review of Derivatives Research, Springer, vol. 3(3), pages 263-282, October.
    14. C. He & J. Kennedy & T. Coleman & P. Forsyth & Y. Li & K. Vetzal, 2006. "Calibration and hedging under jump diffusion," Review of Derivatives Research, Springer, vol. 9(1), pages 1-35, January.
    15. Carverhill, Andrew & Luo, Dan, 2023. "A Bayesian analysis of time-varying jump risk in S&P 500 returns and options," Journal of Financial Markets, Elsevier, vol. 64(C).
    16. J. S. Kennedy & P. A. Forsyth & K. R. Vetzal, 2009. "Dynamic Hedging Under Jump Diffusion with Transaction Costs," Operations Research, INFORMS, vol. 57(3), pages 541-559, June.
    17. de Vette, Nander & Petersen, Annelie & Stan Olijslager, Stan & van Wijnbergen, Sweder, 2018. "What Option Prices tell us about the ECB's Unconventional Monetary Policies," CEPR Discussion Papers 13371, C.E.P.R. Discussion Papers.
    18. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.

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