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Calibration of Stock Betas from Skews of Implied Volatilities

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  • Jean-Pierre Fouque
  • Eli Kollman

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.

Suggested Citation

  • Jean-Pierre Fouque & Eli Kollman, 2011. "Calibration of Stock Betas from Skews of Implied Volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(2), pages 119-137.
    • Handle: RePEc:taf:apmtfi:v:18:y:2011:i:2:p:119-137
    DOI: 10.1080/1350486X.2010.481175
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    Citations

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    Cited by:

    1. Peter Christoffersen & Xuhui (Nick) Pan, 2014. "Equity Portfolio Management Using Option Price Information," CREATES Research Papers 2015-05, Department of Economics and Business Economics, Aarhus University.
    2. Rainer Baule & Olaf Korn & Sven Saßning, 2016. "Which Beta Is Best? On the Information Content of Option†implied Betas," European Financial Management, European Financial Management Association, vol. 22(3), pages 450-483, June.
    3. Ali Safdari-Vaighani & Davood Ahmadian & Roja Javid-Jahromi, 2021. "An Approximation Scheme for Option Pricing Under Two-State Continuous CAPM," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1373-1385, April.
    4. Sofiene El Aoud & Frédéric Abergel, 2014. "Calibration of a stock's beta using options prices," Post-Print hal-01006405, HAL.
    5. 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).
    6. Zhe Li, 2020. "Equity Option Pricing with Systematic and Idiosyncratic Volatility and Jump Risks," JRFM, MDPI, vol. 13(1), pages 1-18, January.

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