Forecasting the volatility of stock price index: A hybrid model integrating LSTM with multiple GARCH-type models

Abstract

Volatility plays crucial roles in financial markets, such as in derivative pricing, portfolio risk management, and hedging strategies. Therefore, accurate prediction of volatility is critical. We propose a new hybrid long short-term memory (LSTM) model to forecast stock price volatility that combines the LSTM model with various generalized autoregressive conditional heteroscedasticity (GARCH)-type models. We use KOSPI 200 index data to discover proposed hybrid models that combine an LSTM with one to three GARCH-type models. In addition, we compare their performance with existing methodologies by analyzing single models, such as the GARCH, exponential GARCH, exponentially weighted moving average, a deep feedforward neural network (DFN), and the LSTM, as well as the hybrid DFN models combining a DFN with one GARCH-type model. Their performance is compared with that of the proposed hybrid LSTM models. We discover that GEW-LSTM, a proposed hybrid model combining the LSTM model with three GARCH-type models, has the lowest prediction errors in terms of mean absolute error (MAE), mean squared error (MSE), heteroscedasticity adjusted MAE (HMAE), and heteroscedasticity adjusted MSE (HMSE). The MAE of GEW-LSTM is 0.0107, which is 37.2% less than that of the E-DFN (0.017), the model combining EGARCH and DFN and the best model among those existing. In addition, the GEW-LSTM has 57.3%, 24.7%, and 48% smaller MSE, HMAE, and HMSE, respectively. The first contribution of this study is its hybrid LSTM model that combines excellent sequential pattern learning with improved prediction performance in stock market volatility. Second, our proposed model markedly enhances prediction performance of the existing literature by combining a neural network model with multiple econometric models rather than only a single econometric model. Finally, the proposed methodology can be extended to various fields as an integrated model combining time-series and neural network models as well as forecasting stock market volatility.