Extreme risk in futures contracts

Abstract

This article uses Extreme Value Theory (EVT) to measure extreme risk in futures contracts with diverging underlying assets. The approach provides a framework for analysing the distributional properties of extreme returns. EVT is statistically robust at estimating Value at Risk (VaR) for different asset classes and at very low probabilities. By way of contrast, the estimation bias by relying on the thin-tailed normal distribution for measuring extreme price movements is illustrated. Back-tests confirm the relative accuracy of the approaches.

Acknowledgements

University College Dublin's Faculty research funding is gratefully acknowledged.

Notes

EVT would be equally suitable for a short position with extreme tail risk similar for the downside and upside of a distribution of returns (Cotter, 2004a).

Stability over time could also be examined (see Cotter, 2004b).

This underestimation bias has practical implications for futures traders, with for example, the extreme price movements associated with the 1987 crash assuming normality predicted to occur every 5900 years. The reality is very different with these loss levels occurring over a much smaller period.