Measuring Asset Dependence with Optimal Transport and Copulas

Summary

The document explains an optimal-transport approach to measuring dependence between asset return series. It first transforms observations into empirical copula coordinates using normalized ranks, which removes marginal scales while retaining dependence structure. It then compares the observed copula with selected reference copulas using an optimal transport distance, a minimum-cost way to move probability mass between distributions. A target/forget coefficient expresses whether observed dependence is closer to specified target patterns or patterns to disregard.

By choosing reference copulas, an analyst can search for forms of nonlinear dependence that ordinary correlation may miss, such as simultaneous positive and negative association or dependence concentrated in particular variations. The examples describe comparing asset pairs with target patterns, including Gaussian and comonotonic dependence. The implementation is limited to bivariate copulas because higher-dimensional computation is burdensome. The method also depends on the chosen target and forget patterns, so results answer a deliberately framed question rather than providing a universal dependence score. The document outlines the method and references prior work but gives no empirical trading-performance results.

Key ideas

• Empirical copulas use normalized ranks to represent dependence independently of marginal scales.
• Optimal transport measures the cost of moving probability mass between an observed copula and a reference copula.
• Target and forget copulas let analysts specify which dependence patterns matter to a question.
• The approach can detect nonlinear dependence structures that a single correlation coefficient may not describe.
• The documented implementation considers bivariate relationships because higher dimensions are computationally demanding.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.