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Option Anomalies and the Pricing Kernel

Author

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  • Christoffersen, Peter

    (McGill University and Copenhagen Business School)

  • Heston, Steven

    (University of MD)

  • Jacobs, Kris

    (University of Houston and McGill University)

Abstract

We generalize the Heston-Nandi (2000) GARCH model to a discrete-time analog of the Heston (1993) stochastic volatility model with a variance risk premium. We show the pricing kernel in these models generalizes the risk-neutralization in Rubinstein (1976) and Brennan (1979). While it is monotonic in the stock return and volatility, its projection onto the stock return is nonmonotonic. A negative risk premium makes it appear U-shaped. We present new semi-parametric evidence to confirm this U-shaped relationship between the risk-neutral and physical probability densities. The new pricing kernel substantially improves our ability to reconcile the time series properties of stock returns with the cross- section of option prices. It provides a unified explanation for the implied volatility puzzle, the overreaction of long-term options to changes in short-term variance, and the fat tails of the risk-neutral return distribution relative to the physical distribution.

Suggested Citation

  • Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    • Handle: RePEc:ecl:upafin:11-17
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    File URL: http://fic.wharton.upenn.edu/fic/papers/11/11-17.pdf
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    2. Bekkour, Lamia & Jin, Xisong & Lehnert, Thorsten & Rasmouki, Fanou & Wolff, Christian, 2015. "Euro at risk: The impact of member countries' credit risk on the stability of the common currency," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 67-83.
    3. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    4. Fousseni Chabi-Yo, 2012. "Pricing Kernels with Stochastic Skewness and Volatility Risk," Management Science, INFORMS, vol. 58(3), pages 624-640, March.

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    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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