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

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

Sukanto Bhattacharya1 and Kuldeep Kumar2

 1 Department of Business Administration, Alaska Pacific University, Anchorage 99508, AK, USA
2School of Business, Bond University, Australia
Received 28 April 2006; Revised 19 October 2006; Accepted 14 November 2006

Recommended by Mahyar A. Amouzegar

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.