金融中的Levy模型及其仿真

运筹学学报 ›› 2013, Vol. 17 ›› Issue (1): 1-9.

• 运筹学 • 下一篇

金融中的Levy模型及其仿真

陈睿迪¹，彭一杰¹，胡建强¹

1. 复旦大学管理科学与工程系

出版日期:2013-03-15 发布日期:2013-03-15
通讯作者: 胡建强 E-mail:hujq@fudan.edu.cn
基金资助:
国家自然科学基金项目(Nos. 71071040, 71028001, 70832002, 71061160506), 上海浦江人才计划项目(No. 09PJ1401500), 上海高校特聘教授(东方学者)岗位计划和上海千人计划岗位资助.

Simulation of Levy-driven models and its application in finance

CHEN Ruidi¹, PENG Yijie¹, HU Jianqiang¹

1. Department of Management Science and Engineering, Fudan University

Online:2013-03-15 Published:2013-03-15
Contact: HU Jianqiang E-mail:hujq@fudan.edu.cn

摘要/Abstract

摘要： 近20年来，金融中Levy模型与蒙特卡洛仿真技术日益受到重视. 在连续时间过程的金融建模中带跳跃的Levy模型相比于连续轨道的布朗运动模型能很好地刻画市场的跳跃，更好地拟合金融数据的统计特征，更准确地对衍生品定价. 但是，相较于经典的Black-Scholes模型，用Levy模型对衍生品定价以及求解对冲策略的计算复杂度大大增加. 蒙特卡洛仿真成为Levy模型计算中最重要的方法之一. 首先详细地介绍了Levy模型引入的背景，并引出仿真方法在其中重要的应用价值. 最后，简要地给出了Levy过程仿真及其梯度估计的基本方法.

关键词: Levy模型, 蒙特卡洛仿真, 仿真优化, 梯度估计

Abstract: Levy processes have been widely used to model financial assets since the 1990s. The reason of their widespread applications is mainly due to the fact that they provide more realistic models that capture discontinuous behaviors and stylized empirical statistical characteristics of time series data in economy and finance. However, when applied to derivative pricing, very few analytical results are available except for European options. Therefore, one usually has to resort to numerical methods such as Monte Carlo simulation method. The simulation method is so attractive that it is very general and can also handle high dimensional problems very well. In this short survey paper, we first provide an overview on Levy processes. We then introduce Monte Carlo simulation method for Levy processes. Finally, we discuss the two main simulation based gradient estimation methods: perturbation analysis and likelihood ratio method.

Key words: Levy-driven model, Monte Carlo simulation, simulation optimization, gradient estimation

陈睿迪，彭一杰，胡建强. 金融中的Levy模型及其仿真[J]. 运筹学学报, 2013, 17(1): 1-9.

CHEN Ruidi, PENG Yijie, HU Jianqiang. Simulation of Levy-driven models and its application in finance[J]. Operations Research Transactions, 2013, 17(1): 1-9.

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金融中的Levy模型及其仿真

Simulation of Levy-driven models and its application in finance

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