Managing financial risk is crucial to guard against systematic risk,while risk management depends on describing stylized facts in stock markets and measuring tail risk.In Chinese stock market,we build 20 Levy-GARCH models to investigate the affect of asymmetry and non-Gaussianity on return prediction and tail risk measurement.We calculate the VaR and CVaR when noises follow jump processes and use fast Fourier transformation and back-testing in empirical research.According to empirical research on the Shanghai Stock Exchange Composite Index,asymmetry and non-Gaussianity are vital characteristics,and jump processes matter in fitting and predicting returns and measuring risks;in tail risk measurement,non-affine GARCH models with jumps outperform affine models,and GARCH models with finite intensity jump process perform better than those with infinite activity jumps.In conclusion,the non-affine Levy-GARCH models with asymmetry and non-Gaussianity perform well in return fitting and tail risk measurement,and jump process with finite intensity can explain tail risk in Chinese stock markets more precisely.