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Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 39460, 15 pages
http://dx.doi.org/10.1155/2007/39460
Research Article

Computational Exploration of the Biological Basis of Black-Scholes Expected Utility Function

1Department of Business Administration, Alaska Pacific University, Anchorage, AK 99508, USA
2School of Business, Bond University, Australia

Received 28 April 2006; Revised 19 October 2006; Accepted 14 November 2006

Academic Editor: Mahyar A. Amouzegar

Copyright © 2007 Sukanto Bhattacharya and Kuldeep Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It has often been argued that there exists an underlying biological basis of utility functions. Taking this line of argument a step further in this paper, we have aimed to computationally demonstrate the biological basis of the Black-Scholes functional form as applied to classical option pricing and hedging theory. The evolutionary optimality of the classical Black-Scholes function has been computationally established by means of a haploid genetic algorithm model. The objective was to minimize the dynamic hedging error for a portfolio of assets that is built to replicate the payoff from a European multi-asset option. The functional form that is seen to evolve over successive generations which best attains this optimization objective is the classical Black-Scholes function extended to a multiasset scenario.

Computational Exploration of the Biological Basis of Black-Scholes Expected Utility Function