Pricing by means of Genetic Programming

This master thesis describes how to price options by means of Genetic Programming. The underlying model is the Generalized Autoregressive Conditional Heteroskedastic (GARCH) asset return process. The goal of this master thesis is to find a closed-form solution for the price of European call options where the underlying securities follow a GARCH process. The data are simulated over a wide range to cover a lot of existing options in one single equation. Genetic Programming is used to generate the pricing function from the data. Genetic Programming is a method of producing programs just by defining a problemdependent fitness function. The resulting equation is found via a heuristic algorithm inspired by natural evolution. Three different methods of bloat control are used. Additionally Automatic Defined Functions (ADFs) and a hybrid approach are tested, too. To ensure that a good configuration setting is used, preliminary testing of many different settings has been done, suggesting that simpler configurations are more successful in this environment. The resulting equation can be used to calculate the price of an option in the given range with minimal errors. This equation is well behaved and can be used in standard spread sheet programs. It offers a wider range of utilization or a higher accuracy, respectively than other existing approaches.