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Empirical study of value‐at‐risk and expected shortfall models with heavy tails

Fotios C. Harmantzis (Stevens Institute of Technology, Hoboken, New Jersey, USA)
Linyan Miao (Stevens Institute of Technology, Hoboken, New Jersey, USA)
Yifan Chien (Stevens Institute of Technology, Hoboken, New Jersey, USA)

Journal of Risk Finance

ISSN: 1526-5943

Article publication date: 1 March 2006



This paper aims to test empirically the performance of different models in measuring VaR and ES in the presence of heavy tails in returns using historical data.


Daily returns of popular indices (S&P500, DAX, CAC, Nikkei, TSE, and FTSE) and currencies (US dollar vs Euro, Yen, Pound, and Canadian dollar) for over ten years are modeled with empirical (or historical), Gaussian, Generalized Pareto (peak over threshold (POT) technique of extreme value theory (EVT)) and Stable Paretian distribution (both symmetric and non‐symmetric). Experimentation on different factors that affect modeling, e.g. rolling window size and confidence level, has been conducted.


In estimating VaR, the results show that models that capture rare events can predict risk more accurately than non‐fat‐tailed models. For ES estimation, the historical model (as expected) and POT method are proved to give more accurate estimations. Gaussian model underestimates ES, while Stable Paretian framework overestimates ES.

Practical implications

Research findings are useful to investors and the way they perceive market risk, risk managers and the way they measure risk and calibrate their models, e.g. shortcomings of VaR, and regulators in central banks.


A comparative, thorough empirical study on a number of financial time series (currencies, indices) that aims to reveal the pros and cons of Gaussian versus fat‐tailed models and Stable Paretian versus EVT, in estimating two popular risk measures (VaR and ES), in the presence of extreme events. The effects of model assumptions on different parameters have also been studied in the paper.



Harmantzis, F.C., Miao, L. and Chien, Y. (2006), "Empirical study of value‐at‐risk and expected shortfall models with heavy tails", Journal of Risk Finance, Vol. 7 No. 2, pp. 117-135.



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