The Analytic Indication,Parameter Estimation And Numerical Calculation Of The Option Price Under The CKLS Model

With the development of the market,a large number of empirical studies show that more and more short-term rate models in capturing the dynamics cannot be described by those classic ones.So the mean-reverting ?–process(CKLS model)has been correspondingly proposed.In most cases,its coefficients do not satisfy the linear growth condition;even they satisfy the local Lipschitz condition.So we still cannot examine existence of solutions by traditional techniques.In this paper,these difficulties have been overcome.First,it is proved that when the parameter? ? 1,there is a local solution to the CKLS equation.Then the globally unique positive solution of the equation is proved by the Lyapunov function method.Second,when the parameter ? ? [1/2,1),we demonstrate the non-negativity of solution and the strong uniqueness through using ? functions.Third,we prove that there is a weak solution of the CKLS equation in the case of the parameter? ? [0,1/2).Finally,the paper applies the CKLS model to empirically analyze the inter-bank lending transaction borrowing rate.The four parameter values of CKLS model are estimated.Then the model is used to predict the future data,and a better prediction result has been obtained.The CKLS model has a high application value.