cCorrGAN: Conditional Correlation GAN for Learning Empirical Conditional Distributions in the Elliptope

TL;DR

This paper introduces cCorrGAN, a conditional GAN approach to model empirical conditional distributions within the correlation matrix space, with applications in finance and a discussion on geometric challenges.

Contribution

The paper presents a novel conditional GAN method tailored for the elliptope of correlation matrices, advancing the modeling of complex dependency structures.

Findings

Effective approximation of conditional correlation distributions

Application to Monte Carlo simulations in finance

Discussion on elliptope geometry limitations

Abstract

We propose a methodology to approximate conditional distributions in the elliptope of correlation matrices based on conditional generative adversarial networks. We illustrate the methodology with an application from quantitative finance: Monte Carlo simulations of correlated returns to compare risk-based portfolio construction methods. Finally, we discuss about current limitations and advocate for further exploration of the elliptope geometry to improve results.