Forecasting Volatility of Stock Index: Deep Learning Model with Likelihood-Based Loss Function

Volatility is widely used in different financial areas, and forecasting the volatility of financial assets can be valuable. In this paper, we use deep neural network (DNN) and long short-term memory (LSTM) model to forecast the volatility of stock index. Most related research studies use distance loss function to train the machine learning models, and they gain two disadvantages. The first one is that they introduce errors when using estimated volatility to be the forecasting target, and the second one is that their models cannot be compared to econometric models fairly. To solve these two problems, we further introduce a likelihood-based loss function to train the deep learning models and test all the models by the likelihood of the test sample. The results show that our deep learning models with likelihood-based loss function can forecast volatility more precisely than the econometric model and the deep learning models with distance loss function, and the LSTM model is the better one in the two deep learning models with likelihood-based loss function.