Stochastic modeling using machine learning and stochastic differential equations
Typ
Examensarbete för masterexamen
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2022
Författare
Johansson, Olof
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Stochastic differential equations, machine learning, stochastic modeling, echo state networks, recurrent neural networks, financial time series