English Version
学院简介 历史沿革 机构设置 现任领导 院长寄语 历任领导 咨询委员会
学科工作 学科采风 科研工作 科研项目 博士后科研流动站
本科教学 专业学位 研究生教学 高端培训 继续教育
招生信息 专业介绍 招聘信息 职业规划 毕业生信息 毕业生去向(Placement of Graduates) EFMD国际人才网
国际交流 合作项目 国际认证 办事指南
学工在线 研究生学工
党建巡礼 学院简报 学习参考 管理制度 教工之家
校友名录 杰出校友 历史名人 MBA联合会 EMBA校友会
 
Lingfei Li, Gongqiu Zhang (张功球)*:Error analysis of finite difference and Markov chain approximations for option pricing

  【Abstract】Mijatović and Pistorius proposed an efficient Markov chain approximation method for pricing European and barrier options in general one-dimensional Markovian models. However, sharp convergence rates of this method for realistic financial payoffs, which are nonsmooth, are rarely available. In this paper, we solve this problem for general one-dimensional diffusion models, which play a fundamental role in financial applications. For such models, the Markov chain approximation method is equivalent to the method of lines using the central difference. Our analysis is based on the spectral representation of the exact solution and the approximate solution. By establishing the convergence rate for the eigenvalues and the eigenfunctions, we obtain sharp convergence rates for the transition density and the price of options with nonsmooth payoffs. In particular, we show that for call-/put-type payoffs, convergence is second order, while for digital-type payoffs, convergence is generally only first order. Furthermore, we provide theoretical justification for two well-known smoothing techniques that can restore second-order convergence for digital-type payoffs and explain oscillations observed in the convergence for options with nonsmooth payoffs. As an extension, we also establish sharp convergence rates for European options for a rich class of Markovian jump models constructed from diffusions via subordination. The theoretical estimates are confirmed using numerical examples.

  【Keywords】 convergence rate; diffusions; European and barrier options; finite difference; Markov chain approximation; nonsmooth payoffs; smoothing techniques; spectral representation; subordination

  本文已被《Mathematical Finance》接收且在线出版,为学院A-类奖励期刊。张功球为本文通讯作者。

  http://onlinelibrary.wiley.com/wol1/doi/10.1111/mafi.12161/abstract

发布时间:2018-01-23 浏览人数:
相关链接
 
查询服务:2018普通本科生转专业成绩查询 | 本科教务系统 | 研究生教务系统 | 科研管理系统 | E科之家 | 工资查询 | 校历查询 | 电话查询 | 交通查询 | 网站管理
相关链接:《经济评论》 | 《珞珈管理评论》 | 《珞珈MBA》 | 《武汉大学EMBA》 | 康腾实践中心