A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification

Estimating Value at Risk and Expected Shortfall Using Expectiles

Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling

An efficient and accurate approach is proposed for forecasting Value at Risk [VaR] and Expected Shortfall [ES] measures in a Bayesian framework. This consists of a new adaptive importance sampling method for Quantile Estimation via Rapid Mixture of t approximations [QERMit]. As a first step the optimal importance density is approximated, after which multi-step ‘high loss’ scenarios are efficien...

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

Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution

A parametric approach to estimating and forecasting Value-at-Risk (VaR) and expected shortfall (ES) for a heteroscedastic financial return series is proposed. The well-known GJR–GARCH form models the volatility process, capturing the leverage effect. To capture potential skewness and heavy tails, the model assumes an asymmetric Laplace form as the conditional distribution of the series. Further...