Garch-M Models With The Case Study Of China Stock Market

The risk premium, as a central concept in financial economics, is of greatsignificance in asset pricing, portfolio option, hedging, derivative pricing and riskmanagement. The level of risk premium can directly indicate the market value of risk,which is helpful for the investors to make the best decision. Especially in China,financial markets have changed beyond recognition over the past few decades; variousfinancial derivatives are emerging in an endless stream; and the market risk becomesmore and more unpredictable. Estimating and predicting the risk premium play animportant role in the research of the microscopic structure of the market and theliquidity of the financial assets, which can help us better grasp the macro market trend.As we all know, the research of risk premium originated from the capital assetpricing theory that investors must be compensated for bearing additional risk. Motivatedby the ICAPM, GARCH-M model was another commonly used tool for modeling therisk premium. However, the GARCH-M model as a parameter model inevitably madestrict assumptions, which may cause a model misspecification. To overcome theseshortcomings, researchers proposed semiparametric GARCH-M models, whoseparameter parts can make good explanation for the models while the nonparametricparts can better capture the characteristics of the data or even reduce the deviation of theestimation.A semiparametric asymmetric GARCH-M model with general nonparametricrisk-return tradeoff and a TGARCH-type underlying volatility is introduced in this paper.According to the idea of two-stage estimate, the mean function is estimated by the localpolynomial and the volatility parameters are obtained via the weighted least squaremethod. Under reasonable assumptions, asymptotic normal distributions are establishedfor the estimators of the model. Then a sampling experiment testifies the accuracy ofour semiparametric method. Finally after applying this method to the China stockmarket, its great outperformance in terms of goodness-fit is found by comparing toparametric models, and the shape of risk premium is certified to be nonlinear andnonmonotonic.