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Calibration of Stock Betas from Skews of Implied Volatilities

Calibration of Stock Betas from Skews of Implied Volatilities 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Calibration of Stock Betas from Skews of Implied Volatilities

Fouque, Jean-Pierre; Kollman, Eli
Applied Mathematical Finance , Volume 18 (2): 19 – Feb 17, 2011
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Calibration of Stock Betas from Skews of Implied Volatilities

Abstract

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...
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Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2010.481175
Publisher site
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Abstract

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.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Feb 17, 2011

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

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