主管:中国科学院
主办:中国优选法统筹法与经济数学研究会
   中国科学院科技战略咨询研究院
论文

基于多层次蒙特卡罗方法的巴黎期权定价

展开
  • 1. 中央财经大学管理科学与工程学院 北京 100081;
    2. 北京航空航天大学管理学院 北京 100191
宋斌(1971-),女(汉族),山西人,中央财经大学管理科学与工程学院投资系,系主任,研究方向:复杂衍生产品的定价与数值计算、倒向随机微分方程在经济与金融中的应用、利率市场微观结构与订单簿建模、利率期限结构建模,E-mail:selviasong@163.com

收稿日期: 2014-12-16

  修回日期: 2015-09-17

  网络出版日期: 2016-02-25

基金资助

教育部人文社会科学研究规划基金(14YJA790048);国家自然科学基金资助青年项目(11301560);国家自然科学基金资助青年项目(71301173)

Pricing Parisian Option by Multi-level Monte Carlo Method

Expand
  • 1. School of Management Science and Engineering, Central University of Finance and Economics, Beijing 100081, China;
    2. School of Management, Beihang University, Beijing 100191, China

Received date: 2014-12-16

  Revised date: 2015-09-17

  Online published: 2016-02-25

摘要

巴黎期权是由障碍期权发展起来的一种复杂的路径依赖期权,其允许期权持有者在标的资产价格满足在某个给定的价格水平(障碍价格)之上或者之下连续或累计停留预先设定的一段时间的条件下,以预先约定的价格(执行价格)买入或卖出某种标的资产。目前巴黎期权定价的主流数值方法有二叉树方法、有限差分法和蒙特卡罗方法。论文的研究结果表明,在给定的精度条件下,与标准蒙特卡罗方法相比,多层蒙特卡罗方法能够将运算成本从O-3)减少到O-2(logε)2);反之,在给定的计算成本条件下,相对于标准蒙特卡罗方法,多层蒙特卡罗方法能够更快地收敛到真值附近。本文将其应用于巴黎期权的定价计算中,增加了巴黎期权的数值算法选择范围,并提高了巴黎期权定价的精度。

本文引用格式

宋斌, 林则夫, 张冰洁 . 基于多层次蒙特卡罗方法的巴黎期权定价[J]. 中国管理科学, 2016 , 24(2) : 11 -18 . DOI: 10.16381/j.cnki.issn1003-207x.2016.02.002

Abstract

Parisian option is a complex path-dependent option extended from the barrier options, which allows the holder buy or sell a certain underlying asset at a pre-specified price under the condition that underlying asset price above or below a given level of a continuous or cumulative occupation time before maturity. The numerical methods for pricing Parisian option include binomial tree method, finite difference method and Monte Carlo method. Compared with other numerical methods, Monte Carlo method is more flexible and easy to implement and improve; moreover, its estimation error and convergence speed has stronger independence with the dimensions of the problem to be solved, and thus can solve the target variable of high-dimensional derivative securities pricing better.In this paper the Parisian option is priced using the Monte Carlo method, and improves the standard Monte Carlo algorithm is improved to multi-level Monte Carlo algorithm. Our research results show that under the given accuracy, multi-level Monte Carlo algorithm can reduce the calculation costs from O-3) to O-2(logε)2) comparing with the standard Monte Carlo method. On the other hand, under given calculation cost, multi-level Monte Carlo method can converge to the true value faster comparing with standard Monte Carlo method. Applying this method to Parisian option pricing not only expanses the choice scope of Parisian options' numerical algorithms, but also improves the precision of Parisian option pricing, and lays a certain foundation for Parisian options' application in the domestic market.

参考文献

[1] Chesney M, Jeanblanc-Picqué M, Yor M. Brownian excursions and Parisian barrier options[J]. Advances in Applied Probability, 1997,29(1):165-184.

[2] Haber R J, Schönbucher P J, Wilmott P. Pricing parisian options[J]. The Journal of Derivatives, 1999, 6(3):71-79.

[3] Vetzal K R, Forsyth P A. Discrete Parisian and delayed barrier options:A general numerical approach[J]. Advances in Futures and Options Research, 1999, 10:1-16.

[4] 宋斌, 周湛满, 魏琳, 等. 巴黎期权的PDE定价及隐性差分方法研究[J]. 系统工程学报, 2013, 28(6):764-774.

[5] Avellaneda M, Wu Lixin. Pricing Parisian-style options with a lattice method[J]. International Journal of Theoretical and Applied Finance, 1999, 2(1):1-16.

[6] Costabile M. A combinatorial approach for pricing Parisian options[J]. Decisions in Economics and Finance, 2002, 25(2):111-125.

[7] Anderluh J H M. Pricing Parisians and barriers by hitting time simulation[J]. European Journal of Finance, 2008, 14(2):137-156.

[8] 郭冬梅, 宋斌, 汪寿阳, 等. 基于停时模拟的移动窗口巴黎期权的定价[J]. 系统工程理论与实践, 2013, 33(3):577-584.

[9] 谭英双, 衡爱民, 龙勇, 等. 模糊环境下不对称企业的技术创新投资期权博弈分析[J]. 中国管理科学, 2011, 19(6):163-168.

[10] Kwok Y K, Lau K W. Pricing algorithms for options with exotic path-dependence[J]. Journal of Derivatives, 2001, 9(1):28-38.

[11] Boyle P P, Broadie M, Glasserman P. Monte Carlo methods for security pricing[J]. Journal of Economic Dynamics and Control, 1997, 21(8):1267-1321.

[12] Bernard C, Boyle P. Monte Carlo methods for pricing discrete Parisian options[J]. The European Journal of Finance, 2011, 17(3):169-196.

[12] Joy C, Boyle P P, Tan K S. Quasi-Monte Carlo methods in numerical finance[J]. Management Science, 1996, 42(6):926-938.

[13] Giles M B. Multilevel Monte Carlo path simulation[J]. Operations Research, 2008, 56(3):607-617.

[14] Giles M B, Higham D J, Mao Xuerong. Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff[J]. Finance and Stochastics, 2009, 13(3):403-413.

[15] Giles M B, Waterhouse B J. Multilevel quasi-Monte Carlo path simulation[J]. Advanced Financial Modeling, Radon Series on Computational and Applied Mathematics, 2009,(8):165-181.

[16] Primozic T. Estimating expected first passage times using multilevel Monte Carlo algorithm. Oxford:Oxford University, 2011.

[17] Kebaier A. Statistical Romberg extrapolation:A new variance reduction method and applications to option pricing[J]. The Annals of Applied Probability, 2005, 15(4):2681-2705.
文章导航

/