Value at Risk and Expected Shortfall for large portfolios

Value-at-Risk and expected shortfall for linear portfolios with elliptically distributed risk factors

In this paper, we generalize the parametric ∆-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distribution.

Dynamic Semiparametric Models for Expected Shortfall (and Value-at-Risk)

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to ...

Estimating Value at Risk and Expected Shortfall Using Expectiles

Expected Shortfall: a natural coherent alternative to Value at Risk

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the “average of the 100p% worst losses” in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representations of ES which turn out to be more appropriate for certain purposes.

Expected Shortfall: a natural coherent alternative to Value at Risk