We present a general framework for testing the accuracy of Value-at-Risk (VaR) forecasts. The approach is based on the observation that violations – the days on which portfolio losses exceed the VaR – should be unpredictable. Specifically, these violations form a martingale difference...

Techniques for simulated maximum likelihood (SML) estimation, filtering, and assessing the fit of stochastic volatility models are examined. Both one- and two-factor models (with leverage effects) are considered. The techniques are computationally efficient, robust, straightforward to implement,...

We introduce SV models with Markov regime changing state equation (SVMRS) to investigate the important properties of volatility, high persistence and smoothness. With the quasi-ML approach proposed in our study, we showed that volatility is far less persistent and smooth than the GARCH or SV...

Filtering techniques are often applied to the estimation of dynamic latent variable models. However, these techniques are often based on a set assumptions which restrict models to be specified in a linear state-space form. Numerical filtering techniques have been propsed that avoid invoking such...

The stochastic volatility (SV) models had not been popular as the ARCH (autoregressive conditional heteroskedasticity) models in practical applications until recent years even though the SV models have close relationship to financial economic theories. The main reason is that the likelihood of...