Operations Management and Econometrics

Bayesian VaR and ES forecasting via the two-sided Weibull distribution

Qian Chen, Discipline of Operations Management and Econometrics

11th Nov 2011  11:00 am - Room 498, Merewether Building (H04)

A study on the impacts of asymmetry in the conditional distribution and volatility on forecasting Value-at-Risk and expected shortfall is carried via parametric method. A new distribution derived from Weibull distribution is proposed to generate adequate Value-at-Risk and expected shortfall. A two-regime double-threshold GARCH is used to model the asymmetric behavior in volatility process of a heteroskedastic financial return series. As the financial data are usually observed in high frequency, a smoother change between regimes is considered more reasonable than a sharp transition. Thus a generalized two-regime smooth-transition GARCH model is adopted for comparison. To allow flexibility in the model, the threshold parameter, at which the change between regimes occurs, is estimated. It???s well known that the financial data are usually observed other than normally distributed. Therefore, a Student t and an asymmetric Laplace distribution are also used as the potential distribution for the financial data. The latter is recently popular as it captures the dynamics in skewness with a time-varying shape parameter. Hansen???s generalized skewed t distribution is also frequently used to take into account the dynamics in skewness. For comparison, this distribution is also used in our models. The model parameters are estimated by Baysian Markov Chain Monte Carlo sampling
scheme, employing the Metropolis-Hastings (MH) algorithm with a mixture of Gaussian proposal distributions. We illustrate the model by applying it to return series from four international stock market indices, as well as two exchange rates, and generating one-step ahead forecasts of VaR and ES. The models are compared via standard and non-standard tests. 

Keywords: Two-sided Weibull, Value-at-Risk, Expected shortfall, Back-testing, precrisis and post crisis, asymmetric higher moments, asymmetric volatility.

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