分数维Hull-White利率模型下基于分数跳-扩散过程的欧式期权定价问题  

European Pricing Options Under Jump-Fraction Process in the Fractional Hull-White Interest Rate Model

作　　者：刘翩 张金良[1] 朱怡梦 LIU Pian;ZHANG Jin-liang;ZHU Yi-meng(School of Mathematics and Statistics,Henan University of Science and Technology,LuoYang 471023,Henan,China)

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471023

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2020年第2期135-141,共7页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51675161)。

摘　　要：利用分数维Ito公式和Δ-对冲技巧,导出了分数维Hull-White利率下原生资产价格服从分数跳-扩散过程的欧式期权定价模型;利用偏微分方程法,求得了该模型的解析解,且导出了上述条件下的欧式看涨期权定价公式、欧式看涨-看跌期权平价公式和欧式看跌期权的定价公式;并由此得到了具相同条件下的欧式数字看涨、看跌期权的定价公式及平价公式。The formulas for the European pricing option under fractional Hull-White interest rate model,in which the underlying asset price obeys the fractional Brownian motion,were obtained by using the fractional Ito formula and the hedging technique.Furthermore,through the partial differential equation method,we obtained the analytical solution of the model and derived the pricing formula of European call option,European option call-put parity relationship under the conditions above mentioned and the pricing formula of European put options.By generalizing the results,the pricing formulas and parity formulas of European call and put digital options with the same conditions as the cases above mentioned were derived.

关 键 词：分数维Hull-White利率模型 分数跳-扩散 期权定价 偏微分方程方法 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]