“Forecasting Stock Index Volatility: A comparison between GARCH and LSTM models”

Abstract

The financial world is characterized by the uncertainty of events and this phenomenon can expose operators to huge financial risks. Thus, there is a need to measure this uncertainty, with the aim to predict it and to make adequate plans of action. The concept of uncertainty is often associated with the definition of volatility, which is a measure of the variation of stock prices of a financial instrument during the time. But modelling volatility is not a trivial task, because of the essence of financial stock prices, which usually present volatility clusters, fat tails, nonnormality and structural breaks in the distribution. A popular class of models able to capture many of these stylized facts is the ARCH/GARCH family. As a matter of fact, a GARCH model is able to explain the time-varying variance and the presence of clusters in the series of the returns. Nevertheless, it requires some constraints on both parameters and distributions of returns to obtain satisfactory results. An attractive solution is given by some mathematical models based on artificial intelligence. Indeed, the artificial neural networks, resembling the human brain, are able to make predictions of future volatility due to their ability to be self-adaptive and to be a universal approximator of any underlying nonlinear function of financial data. The aim of this thesis is to make a comparison between the forecasting capabilities of a GARCH(1,1) model and a Long Short-Term Memory network. In particular, the objective is to predict the volatility of the Dow Jones Industrial Average Index, demonstrating the superiority of the neural network with respect to the well-established GARCH model.