Estimate Value-At-Risk In China’s Stock Market

VaR, the abbreviation of ’Value at Risk’, is defined to be the worst possible loss from an investment over a target horizon and for a given probability level, which presents many advantages for risk measurement, risk control and risk supervision. Although the research and application of VaR in foreign countries have been gradually matured, there are some differences between China and foreign countries when apply VaR to measure risk of China’s stock market, since it has its own unique circumstances. It’s worth studying how to estimate the financial risk of China’s stock market more effectively with VaR method. As a semi-parameter method, quantile regression pays attention to variables’quantiles instead of the distribution of time series, and tries to estimate coefficients based on weighted mean absolute error, which is simply least absolute deviation model (LAD). Quantile regression is applicable for China’s financial time series with leptokurtosis and fat-tail by using an optimization algorithm to estimate VaR, which performs excellent in measuring financial risk. How to establish VaR risk measurement model based on quantile regression with China’s national conditions has a very important theoretical and practical significance.Quantile regression approach is applied to estimate the VaRs of China’s stock market from two aspects in this paper:Firstly, estimate VaR with quantile regression VaR model:Considering that the financial time series usually exhibit leptokurtosis, fat-tail, bias, clustering and leverage in reality, a quantile regression approach is applied to estimate the VaR in this paper. We build the quantile regression VaR model to compute VaR of Shanghai Composite Index, based on GARCH family models and different distributions of the residual. The back-testing is used to evaluate the performance of VaR estimations. The comparisons under various assumptions indicate that the proposed quantile regression VaR model is insensitive to both the model and the distribution of residual, which signifies that the model has excellent applicability. In addition, this paper suggests that the longer the holding period is, the better the performance is.Secondly, estimate VaR with CAViaR method:CAViaR model is usually used to calculate value-at-risk of stock market as a conditional autoregresive method. Considering asymmetric effects of market impact and returns may have an autoregressive mean, this paper proposes many CAViaR improved models, including Asymmetric Indirect TARCH and Indirect GARCH with Autoregressive Mean. Additionally, regarding exogenous explanatory variable selection, we propose CAViaR-Volatility by adding the volatility as an exogenous explanatory variable into model. It draws that improved models perform more effectively on out-of-sample prediction, both the forecast effect and the model stability have been improved. In addition, the forecast effect in the case of1%performs better than5%, it may be explained that extreme news act on risk more obviously. The volatility and shows negative correlation, would decrease with volatility increasing.This research that the VaRs of China’s stock market are estimated based on quantile regression indicates the inference that the quantile regression approach is flexible as it requires no assumptions on the form of return distributions. Quantile regression, instead of estimating the distribution of the returns, models the quantile directly with an optimization algorithm, which shows remarkable robustness when returns have a fat-tailed distribution. The quantile regression VaR model and improved CAViaR models-both based on quantile regression-are applicable for China’s stock market.