The Volatility Forecast Of Rate Of Return Of Stock Index Futures Based On Hidden Markov Models

In the field of current financial mathematics research,the volatility prediction of stock index futures returns is always a challenging problem in financial mathematics theory research.Therefore,how to accurately predict the volatility of stock index futures returns in financial markets is the focus of attention between financial sector and investment institutions.With the development of science and technology,many researchers have made remarkable achievements in the research of return volatility.In recent years,the prediction of return volatility of Hidden Markov Model has also achieved remarkable results.Based on the hidden Markov model,this paper studies the volatility characteristics of stock index futures.Firstly,the basic knowledge and theoretical model of Markov model are summarized,the concept of state variable is introduced,and the ARCH model,EGARCH model,ARIMA model and Hidden Markov model are discussed.At the same time,the relevant assumptions and estimates of the volatility model are discussed in detail,and the types and expressions of the return of stock index futures are discussed and studied.Secondly,the traditional GARCH model is studied and analyzed.Under the assumption of Normal distribution,GED distribution,and t distribution,the parameter estimation of GARCH model and HMM(4)model are studied respectively.On this basis,the theoretical model of Hidden Markov model is studied,and the return volatility model of Hidden Markov model is obtained.Finally,based on the existing relevant theoretical models,this paper uses a new theoretical framework model to study the volatility of stock index futures in financial markets,namely T-HMM.The purpose is to provide investors with theoretical basis forinvestment decision and to avoid financial risks in financial markets.This method is based on the Hidden Markov Model and focuses on the logarithm rate of return.Through the analysis of the daily returns of stock index futures,under the assumption of Normal distribution,GED distribution,and t distribution,the fitting effect of the traditional GARCH model and the improved hidden Markov model are analyzed and compared.The results of data analysis show that the improved Hidden Markov Model(HMM)under t distribution is better than the traditional GARCH model,and sample data are used to test the improved model.This method is helpful to the study of financial market dynamics with HMM and can provide an effective theoretical basis for investment decision making for investment institutions and financial sectors.In addition,it also effectively avoids the financial risk caused by the volatility of stock index futures returns in the financial market.