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

Author

Listed:
  • Guenter Franke

    (Center of Finance and Econometrics)

  • Richard C. Stapleton

    (University of Strathclyde)

  • Marti G. Subrahmanyam

    (Stern School of Business, New York University)

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.

Suggested Citation

  • Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," Finance 9904004, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:9904004
    Note: 30 pages
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    References listed on IDEAS

    as
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