基于摄动理论的障碍期权定价  

The Pricing For the Barriers Options Based on the Perturbation Theory

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,贵阳550025 [2]西北工业大学应用数学系,西安710129

出　　处：《应用数学学报》2015年第1期67-79,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(70471057,71171164);贵州省研究生卓越人才计划(ZYRC字[2014]008);西北工业大学博士论文创新基金(CX2012035)资助项目

摘　　要：通常情况下,期权定价的理论研究均假定股票价格的波动率和期望收益率为常数.本文假定波动率和期望收益率为股票价格的一般函数,并在此基础之上研究了障碍期权定价问题.首先,利用偏微分方程的摄动理论将障碍期权的Black-.Scholes方程分解成一系列常系数抛物方程.其次,通过求解这些常系数抛物方程得到了障碍期权定价问题的一个近似解.最后,通过Feymann-Kac公式给出了近似结论的误差估计,结果表明近似解一致收敛于相应期权价格的精确解.Previous option pricing research typically assumes that the stock volatility and expectation return rate are constant during the life of the option. In this study, we release this assumption such that stock volatility and expectation return rate are the function of stock in option valuation model. And then we study the pricing problem of barrier options. First, the partial differential equations for barrier options are transformed into a series of parabolic equations with constant coefficients by perturbation theory. Second, the approximate pricing formulae of the barrier options are given by solving those parabolic equations. Finally, error estimates of these asymptotic solutions are illustrated by using the Feymann-Kac formula in which the results indicate that the asymptotic solutions uniformly converges to its exact solutions.

关 键 词：摄动理论 近似展开 障碍期权 误差估计 

分 类 号：O175.26[理学—数学] F830.91[理学—基础数学]