Some Remarks on T-copulas

TL;DR

This paper investigates three methods for constructing correlated Student-$t$ variables, focusing on their suitability for financial stress testing and economic capital calculations involving heavy-tailed distributions.

Contribution

It provides a comparative analysis of three methods for generating correlated Student-$t$ variables in the context of financial risk modeling.

Findings

Different methods vary in their suitability for stress testing.

Some methods better preserve tail dependence properties.

Recommendations for selecting appropriate methods in financial applications.

Abstract

We examine three methods of constructing correlated Student-$t$ random variables. Our motivation arises from simulations that utilise heavy-tailed distributions for the purposes of stress testing and economic capital calculations for financial institutions. We make several observations regarding the suitability of the three methods for this purpose.