Symbolic Modeling for financial asset pricing

Abstract

Symbolic Regression is a machine learning technique that discovers an unknown function from its samples. Compared to conventional regression techniques (e.g., linear regression, polynomial regression, etc.), Symbolic Regression does not limit the discovered function to specific forms (e.g., linear functions, polynomials, etc.). Its recent developments are enabling its application to various fields, including both scientific study and engineering research. However, in spite of its flexibility, Symbolic Regression still faces one limitation: given datasets from different systems in the same domain, Symbolic Regression needs to find a distinct function for each dataset, instead of finding a more general yet succinct function that can fit all the datasets through the adjustments of its coefficients. The latter approach, which is termed “Symbolic Modeling” in this work, can be seen as a generalization of Symbolic Regression and has important applications to both academia and industry. This work elucidates Symbolic Modeling and unveils a cutting-edge algorithm, deriving its principles from deep learning and genetic programming. This algorithm is implemented into an application, showcasing its practical utility in the field of financial asset pricing, an integral facet of finance that concentrates on asset valuation. It is shown that Symbolic Modeling compares favorably to existing asset pricing models in multiple aspects.