随机利率下B-S模型基于非参数估计的期权保险精算定价  

The Actuarial Pricing of Option Based on the Nonparametric Estimation for B-S Model under the Stochastic Interest Rates

作　　者：王继霞[1] 王添秀 WANG Jixia;WANG Tianxiu(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《郑州大学学报（理学版）》2018年第3期94-99,共6页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(U1504701);河南师范大学博士启动课题项目(qb15184)

摘　　要：引入服从Hull-White模型的随机利率,讨论了广义B-S模型欧式期权的保险精算定价问题.利用标的资产价格过程的实际概率测度和公平保费原理,得到了在期权有效期内有无红利支付两种情况下,欧式期权的保险精算定价公式.考虑到期权的保险定价问题依赖于未知的模型参数——标的资产价格的波动率、随机利率过程的漂移参数和波动率参数,利用资产价格和随机利率的观测数据,给出了基于模型参数估计的保险精算定价公式,并讨论了所得定价公式的相合性.The actuarial pricing of European option for the general B-S models was studied by introducing the Hull-White stochastic interest rates.According to the physical probability measure of underlying assets and principle of fair premium,the actuarial pricings of European option were obtained under the conditions of paying dividends or without paying during the effective date of option.Considering the actuarial pricing depending on the unknown parameters,the volatility of underlying assets price,the drift parameters and diffusion parameter of the stochastic interest rates processes,the actuarial pricing formula based on the estimations of parameters were given by using the observed data of asses pricing and stochastic interest rates.The consistency of pricing formula was discussed.

关 键 词：保险精算定价 广义B-S模型 Hull-White短期利率模型 欧式期权 估计 相合性 

分 类 号：F224.7[经济管理—国民经济] F830.9