Abstract
Symbolic Regression has been widely used during the last decades for inferring complex models. The foundation of its success is due to the ability to recognize data correlations, defining non-trivial and interpretable models. In this paper, we apply Symbolic Regression to explore possible uses and obstacles for describing stochastic financial processes. Symbolic Regression (SR) with Genetic Programming (GP) is used to extract financial formulas, inspired by the theory of financial stochastic processes and Itô Lemma. For this purpose, we introduce in the model two operators: the derivative and the integral. The experiments are conducted on five market indices that are reliable at defining the evolution of the processes in time: Tokyo Stock Price Index (TOPIX), Standard & Poors 500 Index (SPX), Dow Jones (DJI), FTSE 100 (FTSE) and Nasdaq Composite (NAS). To avoid both trivial and not interpretable results, an error-complexity optimization is accomplished. We perform computational experiments to obtain and investigate simple and accurate financial models. The Pareto Front is used to select between multiple candidates removing the over specified ones. We also test Eureqa as a benchmark to extract invariant equations. The results we obtain highlight the limitations and some pursuable paths in the study of financial processes with SR and GP techniques.
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La Malfa, G., La Malfa, E., Belavkin, R., Pardalos, P.M., Nicosia, G. (2022). Distilling Financial Models by Symbolic Regression. In: Nicosia, G., et al. Machine Learning, Optimization, and Data Science. LOD 2021. Lecture Notes in Computer Science(), vol 13164. Springer, Cham. https://doi.org/10.1007/978-3-030-95470-3_38
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