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Option Prices Under Generalized Pricing Kernels

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  • Bertram Düring
  • Erik Lüders

Abstract

In this paper analytical solutions for European option prices are derived for a class of rather general asset specific pricing kernels (ASPKs) and distributions of the underlying asset. Special cases include underlying assets that are lognormally or log-gamma distributed at expiration date T. These special cases are generalizations of the Black and Scholes (1973) option pricing formula and the Heston (1993) option pricing formula for non-constant elasticity of the ASPK. Analytical solutions for a normally distributed and a uniformly distributed underlying are also derived for the class of general ASPKs. The shape of the implied volatility is analyzed to provide further understanding of the relationship between the shape of the ASPK, the underlying subjective distribution and option prices. The properties of this class of ASPKs are also compared to approaches used in previous empirical studies. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Bertram Düring & Erik Lüders, 2005. "Option Prices Under Generalized Pricing Kernels," Review of Derivatives Research, Springer, vol. 8(2), pages 97-123, August.
    • Handle: RePEc:kap:revdev:v:8:y:2005:i:2:p:97-123
    DOI: 10.1007/s11147-005-3852-x
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    References listed on IDEAS

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    1. Günter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black—Scholes Model and Alternative Characterisations of the Pricing Kernel," Review of Finance, European Finance Association, vol. 3(1), pages 79-102.
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    16. 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-.
    17. Franke, Günter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," CoFE Discussion Papers 99/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
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    1. Franke, Günter & Lüders, Erik, 2006. "Return predictability and stock market crashes in a simple rational expectation models," CoFE Discussion Papers 06/05, University of Konstanz, Center of Finance and Econometrics (CoFE).

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