模型指导的单指标非参数期权定价  

Single-index Nonparametric Adjusting of Semi-parametric Option Pricing Model

作　　者：李庆[1] 杨青龙[1] LI Qing;YANG Qing-long(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Hubei Wuhan 430073,China)

机构地区：[1]中南财经政法大学统计与数学学院

出　　处：《数理统计与管理》2018年第6期1086-1094,共9页Journal of Applied Statistics and Management

基　　金：国家自然科学青年基金项目(11301545)

摘　　要：我们在半参数Black-Scholes期权定价模型基础上提出了新的半参数期权定价模型。本文通过变量变换把期权价格支付函数转化为关于状态价格方程随机误差概率密度函数的积分函数,当概率密度函数为不同形式时得到新的非参数期权定价模型：（1）当概率密度函数为非参数形式时得到了单指标非参数期权定价模型;（2）当概率密度函数为正态分布函数与非参数函数之和时得到单指标非参数修正的半参数期权定价模型,即模型指导的单指标非参数期权定价。最后使用上海证券交易所上证50ETF期权数据,使用变窗宽局部线性估计得到单指标半参数模型效果最好。This thesis establishes the new semiparametric option pricing models under the basement of semiparametric Black-Scholes pricing model. In this thesis, the price function of option about state price probability density function is transformed into the function of probability density function about random variable of state price equation. The first new model, we get the single-index semiparametric option pricing model when the probability density function is nonparametric. The second new model, we get the single-index nonparametric option pricing model based on semiparametric option pricing model. Finally, by the option market data of 50 ETF option in Shanghai stock exchange, we get the conclusion that the single-index semiparametric option pricing model performance best.

关 键 词：半参数期权定价 变窗宽 局部线性估计 误差修正 

分 类 号：F832.5[经济管理—金融学] O212[理学—概率论与数理统计]