Stochastic modeling using machine learning and stochastic differential equations

Abstract

Due to the presence of (unpredictable) fluctuations in the financial market, stochastic models have long been used in various financial applications. In particular, a common application is the forecasting of a given financial time series, for example stock prices. Stock prices are often assumed to follow a Geometric Brownian Motion (GBM), a specific type of stochastic differential equation. Recent studies have demonstrated promising results of using neural networks to parameterize SDEs (referred to as a neural SDE framework). Further studies have demonstrated how machine learning, specifically Recurrent Neural Networks (RNNS), can be used for predicting the future values of time-dependent data. The aim of this thesis was to investigate the possibility of combining a RNN with a neural SDE framework to forecast stock prices. In particular, three different RNNs were used, namely a Long Short-Term Memory (LSTM) model, an Echo State Network (ESN) and a Long- Short Echo State Network (LS-ESN). The results of this thesis showed that the three models considered in this thesis achieved more accurate predictions of stock prices when compared to both a traditional LSTM model and a GBM model. This was showed for both a single stock and also for 100 different stocks, where the latter also was tested for different numbers of predicted time steps ahead.