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Jump and Volatility Risk and Risk Premia: A New Model and Lessons from S&P 500 Options

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  • Pedro Santa-Clara
  • Shu Yan

Abstract

We use a novel pricing model to filter times series of diffusive volatility and jump intensity from S&P 500 index options. These two measures capture the ex-ante risk assessed by investors. We find that both components of risk vary substantially over time, are quite persistent, and correlate with each other and with the stock index. Using a simple general equilibrium model with a representative investor, we translate the filtered measures of ex-ante risk into an ex-ante risk premium. We find that the average premium that compensates the investor for the risks implicit in option prices, 10.1 percent, is about twice the premium required to compensate the same investor for the realized volatility, 5.8 percent. Moreover, the ex-ante equity premium that we uncover is highly volatile, with values between 2 and 32 percent. The component of the premium that corresponds to the jump risk varies between 0 and 12 percent.

Suggested Citation

  • 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.
  • Handle: RePEc:nbr:nberwo:10912
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    Cited by:

    1. George M. Constantinides & Jens Carsten Jackwerth & Stylianos Perrakis, 2009. "Mispricing of S&P 500 Index Options," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1247-1277, March.
    2. Santa-Clara, Pedro & Saretto, Alessio, 2009. "Option strategies: Good deals and margin calls," Journal of Financial Markets, Elsevier, vol. 12(3), pages 391-417, August.
    3. Boes, M.J., 2006. "Index options : Pricing, implied densities and returns," Other publications TiSEM e9ed8a9f-2472-430a-b666-9, Tilburg University, School of Economics and Management.
    4. Brennan, Michael J & LIU, XIAOQUAN & Xia, Yihong, 2005. "Option Pricing Kernels and the ICAPM," University of California at Los Angeles, Anderson Graduate School of Management qt4d90p8ss, Anderson Graduate School of Management, UCLA.
    5. Reinhold Hafner & Martin Wallmeier, 2007. "Volatility as an Asset Class: European Evidence," The European Journal of Finance, Taylor & Francis Journals, vol. 13(7), pages 621-644.
    6. Constantinides, George M. & Jackwerth, Jens Carsten & Perrakis, Stylianos, 2007. "Option Pricing: Real and Risk-Neutral Distributions," MPRA Paper 11637, University Library of Munich, Germany.
    7. Jian Chen & Xiaoquan Liu & Chenghu Ma, 2013. "Risk-neutral and Physical Jumps in Option Pricing," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

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    JEL classification:

    • G1 - Financial Economics - - General Financial Markets

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