Statistical Inference Of Volatility Models In Financial Market

Nowadays,the concept of volatility is quoted in a lot of fields and research.theestimation and prediction of volatility in financial market is one of the importanttopics in financial research field in recent years.Volatility is a very broadconcept,and it can be applied in many fields.It has a great variety of types andcalculational methods. So the study on the volatility model in the financial market hasbecome particularly important.Since the ARCH model is proposed, it is widely concerned byresearchers,especially in the financial field.The GARCH model which is obtained byextending ARCH model is designed for the financial data.It is proposed to explainempirical regularity of high frequency financial data. but the ARCH model and theGARCH model can not reflect the asymmetric phenomenon vastly existing in themarket.Therefore, Zakoian (1994) proposed a threshold GARCH model,it allows theexistence of asymmetry.In the past,we can obtain the maximum likelihood estimation of the parametersof T-GARCH model through the BHHH algorithm and the information matrix ofgradient algorithm.By using the information matrix of gradient algorithm, Zakoianget the estimator of T-GARCH model by a particular case of M-estimator based on acontinuous,right differentiable function.But the BHHH algorithm has somedisadvantages,such as: more time-consuming, the computational efficiency isrelatively poor, more iterative times.and each gradient algorithm hascharacteristics,while the Hessian matrix is relatively obvious advantage and hybridgradient algorithm has more advantages.Therefore,this paper refer to the parameterestimation method of GARCH model,give another parameter estimation method ofthis model by using the Hessian matrix of gradient algorithm and the outer productsmatrix of gradient algorithm. Finally, an application of T-GARCH model in interestrate volatility modeling is introduced and some conclusion and follow-up prospects isgiven.