Vasicek随机利率模型下欧式期权定价的Mellin变换法  

Mellin Transform Method For European Option Pricing with Vasicek Stochastic Interest rate

作　　者：孙娇娇[1] SUN Jiaojiao(College of Mathematical Science, Huaibei Normal University,Huaibei, Anhui 235000,China)

机构地区：[1]淮北师范大学数学科学学院

出　　处：《经济数学》2019年第3期21-26,共6页Journal of Quantitative Economics

基　　金：2018年度安徽省高等学校自然科学研究项目一般项目(KJ2018B01);2017年度安徽省高等学校自然科学研究项目重点项目(KJ2017A379)

摘　　要：运用Feynman-Kac公式和偏微分方程法得到Vasicek随机利率模型下的零息债券价格公式.利用△-对冲方法建立该模型下欧式期权价值满足的偏微分方程模型,并用Mellin变换法求解该偏微分方程,最终得到欧式期权定价公式.从数值算例的结果可以看出Mellin变换法的有效性以及不同参数对期权价值的影响.The formula of zero coupon bond price with Vasicek stochastic interest rate is obtained by using Feynman-Kac formula and partial differential equation method. Based on Δ- hedging method,a partial differential equation model satisfied by European option value is established. Then the Mellin transform techniques are used to solve the partial differential equation. Finally, a closed form solution for the European option is obtained. The numerical results show the effectiveness of Mellin transform and the influence of different parameters on the value of option.

关 键 词：金融数学 Mellin变换法 Vasicek随机利率 偏微分方程 

分 类 号：O211[理学—概率论与数理统计] F830[理学—数学]