Multivariate heavy-tailed models for Value-at-Risk estimation

TL;DR

This paper explores multivariate heavy-tailed distribution models for improved Value-at-Risk estimation, addressing estimation challenges and validating models through backtesting on stock portfolios with derivatives.

Contribution

It introduces multivariate heavy-tailed models with varying tail thickness and evaluates their effectiveness in VaR estimation using real market data.

Findings

Models effectively capture tail risk in portfolios.

Backtesting shows improved VaR accuracy.

Heavy-tailed models outperform traditional methods.

Abstract

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals to have different tail thickness. After a discussion of relevant estimation and simulation issues, we conduct a backtesting study on a set of portfolios containing derivative instruments, using historical US stock price data.