A Neural Network with Shared Dynamics for Multi‐Step Prediction of Value‐at‐Risk and Volatility

We develop a Long Short-Term Memory (LSTM) neural network for the joint prediction of volatility, realized volatility and Value-at-Risk. Regularization by means of pooling the dynamic structure for the different outputs of the models is shown to be a powerful method for improving forecasts and smoothing Value-at-Risk (VaR) estimates. The method is applied to daily and high-frequency returns of the S&P500 index over a period of 25 years.