非线性Black-Scholes模型下阶梯期权定价  

The pricing of step options under the nonlinear Black-Scholes model

作　　者：孙玉东[1] 师义民[2] 童红[1] 

机构地区：[1]贵州民族大学理学院,贵州贵阳550025 [2]西北工业大学应用数学系,陕西西安710072

出　　处：《高校应用数学学报（A辑）》2016年第3期262-272,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(71401134;71571144);贵州省科学技术基金(黔科合J字[2015]2076号);贵州民族大学引进人才科研基金(15XRY005);贵州省研究生卓越人才计划(ZYRC字[2014]008)

摘　　要：在非线性Black-Scholes模型下,研究了阶梯期权定价问题.首先利用多尺度方法,将阶梯期权适合的偏微分方程分解成一系列常系数抛物方程;其次通过计算这些常系数抛物型方程的解,给出了修正障碍期权的近似定价公式;最后利用Feymann-Kac公式分析了近似结论的误差估计.In this paper, the pricing problems of geometric average Asian options are studied under the nonlinear Black-Scholes model. Firstly, the partial differential equations for the Asian options are transformed into a series of parabolic equations with constant coefficients by the perturbation method of single-parameter. Secondly, the approximate pricing formulae of the geometric average Asian options are given by solving those parabolic equations with constant coefficients. Finally, the error estimates of the approximate solutions are given by using Green function.

关 键 词：阶梯期权 非线性Black-Scholes模型 Feymann-Kac公式 误差估计 

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