Varying the VaR for Unconditional and Conditional Environments

TL;DR

This paper develops and compares VaR measures based on extreme value theory for European stock index futures, incorporating both unconditional and conditional models with GARCH filtering, highlighting biases in traditional assumptions.

Contribution

It introduces a robust VaR estimation method using extreme value theory with GARCH filtering for both unconditional and conditional environments, addressing fat-tailed risks.

Findings

Unconditional VaR estimates exhibit biases assuming normality.

Conditional models with GARCH filtering improve tail risk estimation.

Extreme value theory provides statistically robust VaR measures.

Abstract

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.