Abstract
In this paper, we incorporate a GARCH model into an artificial neural network (ANN) for financial volatility modeling and estimate the parameters in Tensorflow. Our goal was to better predict stock volatility. We evaluate the performance of the models using the mean absolute errors of powers of the out-of-sample returns between 2 March 2018 and 28 February 2020. Our results show that our modeling procedure with an ANN can outperform the standard GARCH(1,1) model with standardized Student’s t distribution. Our variable importance analysis shows that Net Debt/EBITA is among the six most important predictor variables in all of the neural network models we have examined. The main contribution of this paper is that we propose a Long Short-Term Memory (LSTM) model with a GARCH framework because LSTM can systematically take into consideration potential nonlinearity in volatility structure at different time points. One of the advantages of our research is that the proposed models are easy to implement because our proposed models can be run in Tensorflow, a Python package that enables fast and automatic optimization. Another advantage is that the proposed models enable variable importance analysis.
Highlights
GARCH models are popular in finance and economic literature
The reason for an Long Short-Term Memory (LSTM) layer with different dense layers in the table is that we would like to see if the difference in dense layers can result in different out-of-the-sample mean absolute error
This paper proposes a GARCH(1,1) model with an LSTM network for conditional variance in order to examine how important neural networks are when modeling stock returns
Summary
GARCH models are popular in finance and economic literature. Bollerslev [1] introduced a GARCH(1,1). The class of GARCH models can incorporate important empirical characteristics of financial asset returns and derivatives, such as jumps, and have a recursive closed form for a conditional moment generating function They noted that the class GARCH model can accommodate dynamic volatility, enabling efficient option pricing and an assessment of risks. Kim and Won [16] proposed a hybrid model integrating LSTM with multiple GARCH-type models to incorporate nonlinearities in the model. There are obvious differences between our proposed models and Kim and Won [16]’s model Their LSTM model inputs include the parameters of GARCH, EGARCH, and EWMA at different times in order to measure the trend factors at different times, indicating that they carried out multiple optimizations for calculation of inputs.
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