A Statistical Recurrent Stochastic Volatility Model for Stock Markets

Abstract

The stochastic volatility (SV) model and its variants are widely used in the financial sector, while recurrent neural network (RNN) models are successfully used in many large-scale industrial applications of deep learning. We combine these two methods in a nontrivial way and propose a model, which we call the statistical recurrent stochastic volatility (SR-SV) model, to capture the dynamics of stochastic volatility. The proposed model is able to capture complex volatility effects, for example, nonlinearity and long-memory auto-dependence, overlooked by the conventional SV models, is statistically interpretable and has an impressive out-of-sample forecast performance. These properties are carefully discussed and illustrated through extensive simulation studies and applications to five international stock index datasets: the German stock index DAX30, the Hong Kong stock index HSI50, the France market index CAC40, the U.S. stock market index SP500 and the Canada market index TSX250. An user-friendly software package together with the examples reported in the article are available at https://github.com/vbayeslab.

Keywords:

• Deep learning
• Financial econometrics
• Recurrent neural networks
• Volatility modeling

Supplementary Materials

The online supplementary materials contain the implementation details of the numerical examples and further empirical results.

Acknowledgments

The authors would like to thank the Associate Editor and two referees for their comments which helped improve both the methodology and presentation of the article.

Notes

1 https://sydneyuni.atlassian.net/wiki/spaces/RC/overview

2 The Oxford-Man Institute, https://realized.oxford-man.ox.ac.uk/

Additional information

Funding

The research of Tran was partially supported by the Australian Research Council’s grant DP200103015.