Conditional returns distributions generated by a GARCH process, which are important for many problems in market risk assessment and portfolio optimization, are typically generated via simulation. This paper extends previous research on analytic moments of GARCH returns distributions in several...

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...

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the...

Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both...

Single-state generalized autoregressive conditional heteroscedasticity (GARCH) models identify only one mechanism governing the response of volatility to market shocks, and the conditional higher moments are constant, unless modelled explicitly. So they neither capture state-dependent behaviour...

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...