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Calibration of Stock Betas from Skews of Implied Volatilities

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  • Jean-Pierre Fouque
  • Eli Kollman
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    Abstract

    We develop call option price approximations for both the market index and an individual asset using a singular perturbation of a continuous-time capital asset pricing model in a stochastic volatility environment. These approximations show the role played by the asset's beta parameter as a component of the parameters of the call option price of the asset. They also show how these parameters, in combination with the parameters of the call option price for the market, can be used to extract the beta parameter. Finally, a calibration technique for the beta parameter is derived using the estimated option price parameters of both the asset and market index. The resulting estimator of the beta parameter is not only simple to implement but has the advantage of being forward looking as it is calibrated from skews of implied volatilities.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.481175
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 18 (2011)
    Issue (Month): 2 ()
    Pages: 119-137

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    Handle: RePEc:taf:apmtfi:v:18:y:2011:i:2:p:119-137

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    Related research

    Keywords: CAPM; stock betas; stochastic volatility; implied volatilities;

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    Cited by:
    1. Sofiene El Aoud & Frédéric Abergel, 2014. "Calibration of a stock's beta using options prices," Working Papers hal-01006405, HAL.
    2. Baule, Rainer & Korn, Olaf & Saßning, Sven, 2013. "Which beta is best? On the information content of option-implied betas," CFR Working Papers 13-11, University of Cologne, Centre for Financial Research (CFR).

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