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An Extended Set of Risk Neutral Valuation Relationships for the Pricing of Contingent Claims

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Abstract

This article establishes an extended set of risk neutral valuation relationships (RNVR's), assuming a representative agent who has an extended power utility function, of the HARA class of utility functions. The utility function of the representative agent displays either increasing, constant or decreasing proportional risk aversion. Aggregate consumption and the random payoff of the underlying asset are bivariate three-parameter lognormal distributed. As an application of the RNVR's, closed-form solutions for the price of a call written on a stock are derived. These include an extra parameter, the threshold parameter, not contained in the Black-Scholes formula.

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Authors and Affiliations

  1. Department of Accounting and Finance, University of Strathclyde, 100 Cathedral Street, Glasgow, G4 OLN

    Antonio Camara

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  1. Antonio Camara
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Camara, A. An Extended Set of Risk Neutral Valuation Relationships for the Pricing of Contingent Claims. Review of Derivatives Research 3, 67–83 (1999). https://doi.org/10.1023/A:1009670114285

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