Climate value at risk and expected shortfall for Bitcoin market

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

Measuring Bond Portfolio Value at Risk and Expected Shortfall in US Treasury Market

This paper measured the value at risk (VaR) and expected shortfall (ES) of the US Treasury yield changes. The US Treasury yield data were tested and found to be not normally distributed. Consequently, the mixture normal model (MNM) was used to improve the delta normal VaR and ES measures. It performed extraordinarily well in all cases, based on bootstrapping and mean square error tests. In addi...

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