When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel
AbstractAn 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.
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Bibliographic InfoPaper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 99-01.
Length: 30 pages
Date of creation: Jan 1999
Date of revision:
Other versions of this item:
- Guntar Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterizations of the Pricing Kernel," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-003, New York University, Leonard N. Stern School of Business-.
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- Franke, Gunter, 1984. " Conditions for Myopic Valuation and Serial Independence of the Market Excess Return in Discrete Time Models," Journal of Finance, American Finance Association, vol. 39(2), pages 425-42, June.
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- Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-47, July.
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