An asymptotic hypothesis test for value-at-risk subadditivity is introduced and studied. The test is derived based on an equivalent formulation of the value-at-risk subadditivity inequality in terms of the distribution of the underlying risks' sum. Its size is considered mathematically, and its...

: Plain or crude Monte Carlo simulation (CMC) is commonly applied for estimating multiperiod tail risk measures such as value-at-risk (VaR) and expected shortfall (ES). After fitting a volatility model to the past history of returns and estimating the conditional distribution of innovations, one...

This study introduces the dynamic Gerber model (DGC) and evaluates its performance in the prediction of Value at Risk (VaR) and Expected Shortfall (ES) compared to alternative parametric, non-parametric and semi-parametric methods for estimating the covariance matrix of returns. Based on ES...

Statistical-based predictions with extreme value theory improve the performance of the risk model not by choosing the model structure that is expected to predict the best but by developing a model whose results are a combination of models with different shapes. Using different ensemble...