The Self-Evolving Logic of Financial Claim Prices

Abstract

In this paper, we use Genetic Programming, anoptimisation technique based on the principles ofnatural selection, to price financial contingentclaims. Compared to the traditional arbitrage-basedapproach, this technique is useful when the underlyingasset dynamics are unknown or when the pricingequations are too complicated to solve analytically.Comparing to other established data-driven optionpricing techniques such as neural networks, impliedbinomial trees, etc., genetic programming has theadvantage of not restricting the structure of thepricing formulae. In addition, because it is very easyto incorporate existing analytical pricing formulasinto the evolutionary process, genetic programming canbe applied in combination with existing pricingmethods. In this paper, we show that geneticprogramming can recover Black-Sholes formula from asimulated data sample of fairly small size. Theapplication to S&P 500 futures options also showpromising results.