Abstract
Expected Shortfall (ES) has been proposed as an alternative, almost coherent, risk measure to Value-at-Risk (VaR), as it considers expected loss beyond VaR. In this paper, we compare the performance of different models in estimating VaR and ES 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). Our backtesting results support the assumption of fat-tailed distributions of asset returns. Several computational issues and effects of factors, i.e. rolling window size and confidence level, are also addressed.
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