Generalized autoregressive conditional heteroskedasticity (GARCH) models are widely used in finance literature because GARCH models take into account the distributions of financial returns. In recent years, researchers have been proposing nonlinear approaches because a standard GARCH model does not assume nonlinearity. This thesis presents three studies about financial returns in deep learning framework because deep learning models have nonlinear activation functions. The goals of this chapter are to understand the deep learning models, investigate the correlations between stocks and propose models that have high predictive power.

First, we propose neural networks for univariate daily returns. Similar to GARCH models, the univariate return follows Student’s t distribution. But the mean, variance and degree of freedom in the distribution are modeled by nonlinear deep neural network. The deep neural network assumes that the current return depends on the information over the previous 20 days. We discuss the prediction accuracy of the out-of-sample returns for six possible network models and find that some of the neural networks can outperform a standard GARCH model.

Second, we propose neural networks for multivariate daily returns. We apply modified Cholesky decomposition on the covariance matrix of the returns. After that, we model the parameters by using deep network. The deep neural network assumes that the current return depends on the information over the previous 20 days. We find that our models generate higher mean portfolio returns than Dynamic Conditional Correlation Multivariate GARCH model in all scenarios.

Third, we consider a model with two-step estimation for multivariate intraday returns. In the first step, the deep neural network predicts the standard deviation and mean of returns. In the second step, vine copulas predict correlations. We find that our models outperform equally weighted portfolio.