Bayesian inference and model comparison for asymmetric smooth transition heteroskedastic models

International Journal of Forecasting

Gerlach

Hwang

et al. 2012

Self Cite

Value-at-Risk (VaR) is commonly used for financial risk measurement. It has recently become even more important, especially during the 2008-09 global financial crisis. We propose some novel nonlinear threshold conditional autoregressive VaR (CAViaR) models that incorporate intra-day price ranges. Model estimation and inference are performed using the Bayesian approach via the link with the Skewed-Laplace distribution. We examine how a range of risk models perform during the 2008-09 financial crisis, and evaluate how the crisis affects the performance of risk models via forecasting VaR. Empirical analysis is conducted on five Asia-Pacific Economic Cooperation stock market indices as well as two exchange rate series. We examine violation rates, back-testing criteria, market risk charges and quantile loss function values to measure and assess the forecasting performance of a variety of risk models. The proposed threshold CAViaR model, incorporating range information, is shown to forecast VaR more efficiently than other models, across the series considered, which should be useful for financial practitioners.

Section: Parametric Garch Estimationmentioning

confidence: 99%

Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range

International Journal of Forecasting

Gerlach

Hwang

et al. 2012

Self Cite

“…van Dijk et al (2002) gave a comprehensive review of the smooth transition autoregressive (STAR) model. Recently, Gerlach and Chen (2008) further incorporated smooth transition functions into autoregressive conditional heteroskedastic models to allow for smooth nonlinearity in mean and asymmetry in volatility. It is thus worthwhile to develop smooth transition CAPM-GARCH models to study smooth nonlinearity of the market betas in CAPM.…”

Section: Introductionmentioning

confidence: 99%

Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity

Lin

2011

Comput Econ

Self Cite

Capital asset pricing model (CAPM) has become a fundamental tool in finance for assessing the cost of capital, risk management, portfolio diversification and other financial assets. It is generally believed that the market risks of the assets, often denoted by a beta coefficient, should change over time. In this paper, we model timevarying market betas in CAPM by a smooth transition regime switching CAPM with heteroscedasticity, which provides flexible nonlinear representation of market betas as well as flexible asymmetry and clustering in volatility. We also employ the quantile regression to investigate the nonlinear behavior in the market betas and volatility under various market conditions represented by different quantile levels. Parameter estimation is done by a Bayesian approach. Finally, we analyze some Dow Jones Industrial stocks to demonstrate our proposed models. The model selection method shows that the proposed smooth transition quantile CAPM-GARCH model is strongly preferred over a sharp threshold transition and a symmetric CAPM-GARCH model.

“…Gerlach and Chen (2008) illustrated the efficiency and speed of mixing gains from employing an adaptive scheme where iterates in the burn-in period, simulated from standard random walk Metropolis methods with tuning to achieve desired acceptance rates, are used to build a Gaussian proposal density for use in the sampling period. Chen et al (2011) extended this method to cover a mixture of Gaussian proposals, both in the burn-in and sampling periods.…”

Section: Bayesian Estimation Methodsmentioning

confidence: 99%

“…The most general volatility model considered is a two regime smooth transition nonlinear (ST-)GARCH model, similar to that in Gerlach and Chen (2008). As the data considered are observed daily, such a smooth change between regimes is potentially more reasonable than a sharp regime transition, as in a T-GARCH, though both will be considered and compared.…”

Section: Volatility Modelsmentioning

confidence: 99%

“…: the Exponential-GARCH model of Nelson (1991) and the GJR-GARCH (GJR) model of Glosten, Jagannathan and Runkle (1993), which capture the asymmetric volatility effect of Black (1976). More recently, fully nonlinear GARCH models have been specified, including the threshold (T)-GARCH of Zakoian (1994), the double threshold (DT)-ARCH of Li and Li (1996); the DT-GARCH of Brooks (2001) and the smooth transition (ST-)GARCH of Gonzalez-Rivera (1998) and Gerlach and Chen (2008). Many other models have been proposed that are far too numerous to mention.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The two-sided Weibull distribution and forecasting financial tail risk

International Journal of Forecasting

Gerlach

2013

A two-sided Weibull is developed to model the conditional financial return distribution, for the purpose of forecasting Value at Risk (VaR) and conditional VaR. A range of conditional return distributions are combined with four volatility specifications to forecast tail risk in four international markets, two exchange rates and one individual asset series, over a four year forecast period that includes the recent global financial crisis. The two-sided Weibull performs at least as well as other distributions for VaR forecasting, but performs most favourably for conditional Value at Risk forecasting, prior to as well as during and after the recent crisis. A range of conditional return distributions are combined with four volatility specifications to forecast tail risk in four international markets, two exchange rates and one individual asset series, over a four year forecast period that includes the recent global financial crisis. The two-sided Weibull performs at least as well as other distributions for VaR forecasting, but performs most favourably for conditional Value at Risk forecasting, prior to as well as during and after the recent crisis.