基于摄动方法的关卡期权定价及其误差分析  

Barrier Options' Pricing and Its Error Analysis Based on Perturbation Method

作　　者：董艳[1] DONG Yan(Department of Basic,Shaanxi Railway Institute,Weinan 714000)

机构地区：[1]陕西铁路工程职业技术学院基础部,渭南714000

出　　处：《工程数学学报》2018年第4期375-384,共10页Chinese Journal of Engineering Mathematics

基　　金：陕西铁路工程职业技术学院科研基金项目(KY2016-04)~~

摘　　要：关卡期权定价问题是现代金融学领域研究的热点之一,也是数理金融学的一个重要研究方向.本文在非线性Black-Scholes模型下,研究了关卡期权定价问题.首先,利用扰动理论中单参数摄动展开方法,给出了关卡期权的近似定价公式.其次,在给定的条件下,利用Feyman-Kac公式分析了近似定价公式的误差估计问题.最后,利用数值实验验证了理论分析的近似结果和误差估计的准确性.The Barrier option pricing problem is one of hot topics in modern nance,and also one of important elds in Mathematical nance.In this paper,the pricing problems of barrier options are discussed under the nonlinear Black-Scholes model.Firstly,the author uses the perturbation method of single-parameter to obtain asymptomatic formulae of barrier options pricing problems.Secondly,error estimates of these asymptotic solutions are illustrated by using the Feymann-Kac formula under the given condition.Finally,numerical experiments conrm the correctness of the proposed theoretical results as well as error estimation.

关 键 词：非线性Black-Scholes模型 关卡期权 近似定价公式 误差分析 

分 类 号：F830.9[经济管理—金融学] O211.6[理学—概率论与数理统计]