Volatility Forecastion Via Hidden Markov Models

We can find from the quantification research process of modern finance, volatility hasalways been the core issue of financial theory, therefore, how does the volatility measure andpredict market accurately, becomes the focus of the theoretical and practical circles.Development of modern econometric methodology provides a solid methodological basis forthe modeling of volatility and the volatility models made remarkable progress with efforts ofmany experts and scholars. The Hidden Markov model (HMM) developed in recent years isparticularly effective.The Hidden Markov model consists of two parts, the Markov chain and random process,and a State Space model can be used to represent HMM. The Markov chain used to describethe unobservable states, described by state equation in the State Space model; generalstochastic processes used to describe the relationship between the observed values andunobserved states, this article will let return rate be the observed values, the measurementequation in the state space model to characterize it. In general, the number of parameters willincrease with the number of states of Markov chain, so that if there are a large number ofstates, parameter estimation is known as a very complex problem. This paper uses a specialkind of parameters process, which not only responses the characteristics of market volatilitywell, but also the number of parameters independent of the number of the Markov chain states.In this paper, Hidden Markov model is used to forecast volatility, the volatility is drivenby a Markov process, the return rate is the observed value. Historical market data is used toestimate parameters, and then use the parameters and current observations, to predict futurevolatility. In order to verify the validity of the model, we compared the result with the actualsituation, and the GARCH and EGARCH model are used as comparison models. Theempirical results show the effectiveness of HMM.