一类短期利率模型的最优估计、选择与定价应用

An Optimal Estimation,Selection and Application of the Short-term Interest Rate Models for Stock Option

对CKLS的一般无约束模型进行了推广,提出了两个更为一般的无嵌套短期利率模型,并以中国银行间债券市场国债回购利率R 007的日数据为样本,对这两个模型以及可嵌套在CKLS框架下的GBM模型、V asicek模型和C IR SR模型的欧拉离散化形式进行了极大似然估计(M LE)。在此基础上,采用对数似然比和V uong检验统计量,对它们的模型拟合效果进行了比较,结果表明对CKLS模型推广的第二种形式(模型5)优于其他四个模型。然后,又利用间接推断方法对模型5估计得到的初始参数值的偏差进行校正,并将修正后的参数估计值及其短期利率扩散模型用于对某上市公司的股票看涨期权进行定价。

Based on generalized CKLS model, the paper proposes two more general non-nested short-term interest rate models and estimates the parameters of these two models and three nested models including GBM model, Vasicek model and CIR SR model according to their Euler＇s discretized forms by maximum likelihood estimation with the data sample of China＇s inter-bank bond market government bond repo rate R007. Secondly, by utilizing the log likelihood ratio and Vuong test statistics, the paper compares these models＇ descriptive power for the interest rate change behavior, and the result shows that model 5 is preferable to the other four models. Furthermore, the bias of initial parameter values of model 5 is corrected by indirect inference method. At last, the paper, according to the corrected parameters＇ value as well as the short-term diffusion model 5, prices a corporation＇ s stock call option when interest rate vary with time and obtains the option＇s values corresponding to two exercise prices.