A Comparative Study of GARCH, Stochastic Volatility, and Hybrid LSTM Models across market regimes

Sammanfattning

This study examines whether the canonical stochastic volatility (SV) model outperforms the standard GARCH(1,1) model across different market regimes, and whether relatively simple hybrid LSTM extensions improve forecasting accuracy. Using daily data from the Dow Jones, S&P 500, and FTSE 100 indices, volatility forecasts are evaluated on the stressed exogenous COVID-19 crisis, as well as a calm market period. The results indicate that model performance depends on the market regime. During the stressed COVID-19 period, the GARCH(1,1) consistently achieves slightly lower forecasting errors compared to the SV model. In calmer market conditions, forecasting errors are smaller overall and no specific model demonstrates a clear advantage over the other. The hybrid models are also evaluated across both regimes. The GARCH(1,1)-LSTM specification improves forecasting in several cases, although the gains are comparatively small. In contrast, the SV-LSTM hybrid does not outperform the baseline SV model in any of the datasets. Overall, the findings suggest that hybrid volatility models are not universally superior and that forecasting performance is closely linked to model structure, market characteristics, and the complexity of the hybrid specification.