It is widely accepted that some of the most accurate predictions of aggregated asset returns are based on an appropriately specified GARCH process. As the forecast horizon is greater than the frequency of the GARCH model, such predictions either require time-consuming simulations or they can be...

The estimation of risk at extreme levels of significance (such as 0.1%) can be crucial to capture the losses during market downturns, such as the global financial crisis and the COVID-19 market crash. For many existing models, it is challenging to estimate risk at extreme levels of significance....

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. A new class of rectangular orthogonal matrices is fundamental to the methodology, and these "L-matrices'' can be deterministic, parametric or data specific in nature. The...