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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 S. Bates, 2001. "The Market for Crash Risk," NBER Working Papers 8557, National Bureau of Economic Research, Inc.
    4. repec:wsi:ijtafx:v:18:y:2015:i:04:n:s0219024915500247 is not listed on IDEAS
    5. Mark Broadie & Mikhail Chernov & Michael Johannes, 2009. "Understanding Index Option Returns," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4493-4529, November.
    6. 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.
    7. 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.
    8. Adrien Verdelhan & Hanno Lustig, 2016. "Does Incomplete Spanning in International Financial Markets Help to Explain Exchange Rates?," 2016 Meeting Papers 1183, Society for Economic Dynamics.
    9. Hanno Lustig & Adrien Verdelhan, 2016. "Does Incomplete Spanning in International Financial Markets Help to Explain Exchange Rates?," NBER Working Papers 22023, National Bureau of Economic Research, Inc.
    10. 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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