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Option Valuation with Conditional Heteroskedasticity and Non-Normality
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Option Valuation with Conditional Heteroskedasticity and Non-Normality

Author

Listed:
  • Peter Christoffersen

    (McGill University and CREATES)

  • Redouane Elkamhi

    (University of Iowa)

  • Bruno Feunou

    (Duke University)

  • Kris Jacobs

    (McGill University and Tilburg University)

Abstract

We provide results for the valuation of European style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite state-space setup using the no-arbitrage principle and an equivalent martingale measure. Our approach allows for general forms of heteroskedasticity in returns, and valuation results for homoskedastic processes can be obtained as a special case. It also allows for conditional non-normal return innovations, which is critically important because heteroskedasticity alone does not suffice to capture the option smirk. We analyze a class of equivalent martingale measures for which the resulting risk-neutral return dynamics are from the same family of distributions as the physical return dynamics. In this case, our framework nests the valuation results obtained by Duan (1995) and Heston and Nandi (2000) by allowing for a time-varying price of risk and non-normal innovations. We provide extensions of these results to more general equivalent martingale measures and to discrete time stochastic volatility models, and we analyze the relation between our results and those obtained for continuous time models.

Suggested Citation

  • Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2009. "Option Valuation with Conditional Heteroskedasticity and Non-Normality," CREATES Research Papers 2009-33, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2009-33
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    References listed on IDEAS

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    More about this item

    Keywords

    GARCH; risk-neutral valuation; no-arbitrage; non-normal innovations;
    All these keywords.

    JEL classification:

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

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