Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements

TL;DR

This paper develops and applies extreme spectral risk measures using EV-GP distributions to estimate tail risks of major futures indices, comparing their effectiveness to traditional measures for margin setting.

Contribution

It introduces a novel application of EV-GP-based spectral risk measures to futures markets and evaluates their advantages over VaR, ES, and SPAN in margin requirement contexts.

Findings

Spectral risk measures provide more coherent risk assessments than VaR.

EV-GP tail estimators improve accuracy of extreme risk estimates.

Spectral measures outperform traditional methods in margin setting simulations.

Abstract

This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user's risk-aversion function. It compares these to VaR and Expected Shortfall (ES) risk measures, and compares the precision of their estimators. It also discusses the usefulness of these risk measures in the context of clearinghouses setting initial margin requirements, and compares these to the SPAN measures typically used. Keywords: Spectral risk measures, Expected Shortfall, Value at Risk, Extreme Value