When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel

Guenter Franke, Richard C. Stapleton and Marti G. Subrahmanyam
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Guenter Franke: Center of Finance and Econometrics
Richard C. Stapleton: University of Strathclyde
Marti G. Subrahmanyam: Stern School of Business, New York University

Finance from University Library of Munich, Germany

Abstract: An important determinant of option prices is the elasticity of the pricing kernel used to price all claims in the economy. In this paper, we first show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the stochastic process followed by the underlying asset. Given that the underlying information process follows a geometric Brownian motion, we demonstrate that constant elasticity of the pricing kernel is equivalent to a Brownian Motion for the forward price of the underlying asset, so that the Black- Scholes formula correctly prices options on the asset. In contrast, declining elasticity implies that the forward price process is no longer a Brownian motion: it has higher volatility and exhibits autocorrelation. In this case, the Black-Scholes formula underprices all options.

JEL-codes: G (search for similar items in EconPapers)
Pages: 30 pages
Date: 1999-04-14
Note: 30 pages
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (34)

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