The self-evolving logic of financial claim prices

In this chapter, we will price financial claims by allowing option pricing programs to evolve trough time via combining with each other, mutating randomly, and reproducing at rates based on the pressure of evolutionary selection. The specific technique we employ is Genetic Programming, an optimization technique based on the principles of natural selection. Compared to the traditional arbitrage-based approach, this technique is useful when the underlying asset dynamics are unknown or when the pricing equations are too complicated to solve analytically. Compared to other established data-driven option pricing techniques such as neural networks, implied binomial trees, etc., genetic programming has the advantage of not restricting the structure of the pricing formulas, formulae themselves evolve rather than simply the parameters of a single formula. Our analysis is preliminary. However, by showing that genetic programming can recover Black-Sholes formula from a fairly small data sample, we hope to validate the ability of genetic programming approaches to consistently and efficiently estimate option prices, at least in structurally simple environments. Future research will apply genetic programming approach to more intractable problems in derivative asset pricing.