Review of Derivatives Research

, Volume 8, Issue 2, pp 97–123

Option Prices Under Generalized Pricing Kernels



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.


pricing kernel option pricing partial differential equation finite differences implied volatility 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Institut für MathematikJ. Gutenberg-Universität MainzMainzGermany
  2. 2.Département de finance et assuranceUniversité LavalQuebecCanada

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