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

TL;DR

This paper introduces a dimension reduction approach using Sliced Inverse Regression for parameter estimation in multidimensional stochastic differential equations, with a focus on the Heston model to improve computational efficiency.

Contribution

It proposes a novel application of sliced inference to reduce parameter space complexity in stochastic differential equations, specifically targeting the Heston model.

Findings

Reduced computational costs in parameter estimation.

Effective dimension reduction in the Heston model.

Enhanced inference accuracy with sliced inverse regression.

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.