Portfolio VaR Forecast Based On GAS-Copula Model

Accurate measurement of risk is the basis and premise of financial risk management.Since the concept of VaR is simple and easy to understand and it can integrate the various risks of assets into a simple number,VaR has become the mainstream method of market risk measurement.VaR is quite mature in the measurement of single asset risk,but it also faces great challenges in portfolio risk measurement.The returns of financial assets often show the characteristics of fat tail,skewness,time-varying volatility,tail dependence and time-varying dependence.The traditional VaR measurement models cannot describe these shape and dynamic characteristics.The Copula theory and GAS theory can well describe these characteristics because the Copula theory provides a flexible method to construct joint distribution and the emerging GAS theory provides a unified modeling method for time-varying parameters.In the model building,in order to reflect the role of different features in the portfolio VaR forecast,32 joint distribution models are constructed by combining the four marginal distributions(normal,t,skewed normal and skewed t distributions),two copula functions(normal and t copula functions),two volatility models(constant and GAS volatility models)and two correlation models(constant and GAS correlation models).In the empirical analysis,six cninfo style indices and nine sets of weights are selected to construct 135 two-dimensional portfolios.Monte Carlo simulation and rolling prediction method are used to calculate the VaR of long positions and short positions at the 20 quantile levels.Finally,the performance of different models in the VaR forecast is compared by the unconditional coverage,independence and conditional coverage tests.The empirical results show that: first,the GAS volatility model with skewed t distribution can be used to describe the characteristics of fat tail,skewness and time-varying volatility,and it has obvious advantages in the marginal distribution fitting and VaR prediction.Second,the GAS correlation model with t copula can be used to describe the characteristics of tail dependence and time-varying dependence,and has obvious advantages in the dependence structure fitting,but it has no obvious advantage in VaR prediction.Third,taking into account the computational burden and VaR prediction results,a relatively reasonable choice is that GAS volatility model with skewed t distribution is used as the marginal distribution model,and the static normal copula model is used to describe the dependence structure.