Using Extreme Value Theory to Estimate Value at Risk (Case Study: Foreign Exchange rate)

Document Type : Research Paper

Authors

Yazd University, yazd, Iran

Abstract

This paper examines the extreme value theory as a useful measure for evaluation of extreme risk events (rare but high impact events). A common practice to calculate Value at Risk (VaR) is based on the assumption that changes in the value of the portfolio are normally distributed. However, assets returns usually come from fat-tailed distributions. Therefore, computing VaR under the assumption of conditional normality can be an important source of error. Extreme value theory does not follow from the central limit theorem in mathematics, and instead is focused on extreme data. Therefore, this study examines the extreme value theory is a powerful framework for studying tail distributions. USD return and volatility is considered as a case study in this article. The normality assumption was rejected by examining the distribution of logarithmic returns. The results suggest that the application of EVT make better fit than the other models that are based on the assumption of normality.

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References

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Journal of Asset Management and Financing
Volume 4, Issue 2 - Serial Number 13
September 2016
Pages 77-94

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