Modeling and predicting Chinese stock downside risks via Gaussian mixture models and marked self-exciting point process

Abstract

The downside risks in stock markets may lead to huge losses and bring profound impact on businesses and governments. In order to model and predict these risks in Chinese stock markets, we propose using Gaussian mixture model to fit the risks within a given threshold, while fitting the extreme risks exceeding the threshold with a marked self-exciting point process. In the simulation study, we establish the consistencies of estimators and evaluate the performances of our proposed models by the accuracy of predicted VaR. Finally we apply our proposed models to analyze the behaviors of four real data sets. In order to illustrate our proposed approach can obtain an improved estimate for the VaR, CAViaR and the GARCH-EVT models are chosen for comparative analysis. The analysis shows that our proposed model have better performances than its competitors.

Keywords:

• Autoregressive conditional duration model
• Gaussian mixture model
• generalized Pareto distribution
• marked self-exciting point process
• peaks over threshold model

Mathematics Subject Classification (2000):

• 62G32
• 91B84

Additional information

Funding

This work was supported by the National Nature Science Foundation of China (71871208, 71971204) and the Anhui Provincial Natural Science Foundation (1908085MG236, gxbjzD54).