Hidden Markov model-based modeling and prediction for implied volatility surface

The implied volatility plays a pivotal role in the options market, and a collection of implied volatilities across strike and maturity is known as the implied volatility surface (IVS). To capture the dynamics of IVS, this study examines the latent states of IVS and their relationship based on the regime-switching framework of the hidden Markov model (HMM). The cross-sectional models are first built for daily implied volatilities, and the obtained regression factors are regarded as the proxies of the IVS. Then, having these latent factors, the HMM is employed to model the dynamics of IVS. Take the advantages of HMM, the hidden state for each daily data is identified to achieve the corresponding time distribution, the characteristics, and the transition between the hidden states. The empirical study is conducted on the Shanghai 50ETF options, and the analysis results indicate that the HMM can capture the latent factors of IVS. The achieved states reflect different financial characteristics, and some of their typical features and transfer are associated with certain events. In addition, the HMM exploited to predict the regression factors of the cross-sectional models enables the further forecasting of implied volatilities. The autoregressive integrated moving average model, the vector auto-regression model, and the support vector regression model are regarded as benchmarks for comparison. The results show that the HMM performs better in the implied volatility prediction compared with other models.