Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?

TL;DR

This study empirically compares the impact of marginals and copulas on model risk in multivariate risk forecasting, finding copulas contribute most to risk and proposing a model confidence set approach to mitigate this risk.

Contribution

It provides the first comprehensive empirical analysis of model risk sources in Copula-GARCH models and introduces a method to reduce this risk using model confidence sets.

Findings

Model risk is economically significant and peaks during crises.

Most of the model risk stems from the choice of copula.

Using model confidence sets improves forecast accuracy.

Abstract

Copulas. We study the model risk of multivariate risk models in a comprehensive empirical study on Copula-GARCH models used for forecasting Value-at-Risk and Expected Shortfall. To determine whether model risk inherent in the forecasting of portfolio risk is caused by the candidate marginal or copula models, we analyze different groups of models in which we fix either the marginals, the copula, or neither. Model risk is economically significant, is especially high during periods of crisis, and is almost completely due to the choice of the copula. We then propose the use of the model confidence set procedure to narrow down the set of available models and reduce model risk for Copula-GARCH risk models. Our proposed approach leads to a significant improvement in the mean absolute deviation of one day ahead forecasts by our various candidate risk models.