Option pricing based on HMM and GARCH model

Abstract

This paper aims to improve the accuracy of option pricing by using the hidden Markov model(HMM) incorporated into Black-Scholes option pricing(BS). Considering that volatility forecast is a key issue for option pricing, we firstly use historical time series of the underlying asset to train a two-state HMM. Then we apply the model to recognize the hidden states behind the observable time series, dividing the entire time series into two regimes with different volatility levels. Within each regime, we train the corresponding generalized autoregressive conditional heteroskedasticity(GARCH) model with different parameters. Finally we can predict the hidden state of next time by the HMM and use the corresponding GARCH model to forecast the volatility. After obtaining the volatility sequence during the life of the option, we can further make the forecast on option price based on BS model. The empirical analysis shows that our method is superior to traditional historical volatility and GARCH methods.