The Approach of Sliced Inference in Systems of Stochastic Differential Equations with Comments on the Heston Model

Abstract

Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality, however, comes with a larger parameter space to estimate. Therefore, via a dimension reduction method, Sliced Inverse Regression, we aim to reduce high-dimensional parameter space to a reduced feature space and aim to estimate the parameters on this new featured space rather than using full data structure to lower computational costs. For this study, we closely study the Heston model, and remark our methodology of inference on this chosen model.