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高校应用数学学报
高校应用数学学报  2016, Vol. 31 Issue (4): 390-404    
    
Markov调制Levy模型定价的Fourier-Cos方法
王春发1,2, 陈荣达1,2
1. 浙江财经大学 金融学院, 浙江杭州 310019
2. 浙江财经大学 财富管理与量化投资协同创新中心, 浙江杭州 310019
Option pricing in Markov regime switching Levy models using Fourier-Cosine expansions
WANG Chun-fa1,2, CHEN Rong-da1,2
1. School of Finance, Zhej. Univ. of Fin. and Econ., Hangzhou 310018, China
2. Coor. Innov. Cent. Quant. Invest., Zhej. Univ. Fin. and Econ., Hangzhou 310018, China
 全文: PDF 
摘要： 对一般的Markov调制Levy模型, 利用Fourier Cosine级数展开原理得到欧式期权价格的计算方法. 进一步, 为了改进期权定价的Fourier Cosine级数展开方法的计算精度, Fourier Cosine级数展开的对象进行了修正, 获得了欧式期权价格的修正Fourier Cosine级数展开计算方法. 此外, 还将获得的方法应用于Markov调制Black-Scholes模型, Markov调制Merton跳扩散模型和Markov调制CGMY Levy模型期权定价的计算.具体的数值计算说明: 修正Fourier Cosine级数展开方法应与Fourier Cosine级数展开方法相比, 收敛速度要慢一些, 但准确性却有很大的提高. 特别是对Markov调制纯跳模型, 效果更为显著.
关键词： Levy过程;  Markov调制;  Fourier变换;  Fourier Cosine级数展开;  期权定价    
Abstract: A method of calculating price of European options is obtained via Fourier-Cosine expansions approach when the underlying asset price follows a very general state-dependent regime-switching Levy process. Furthermore, in order to improve accurate of the Fourier-Cosine expansions, a modified Fourier-Cosine expansions is developed. The method is then applied to option pricing for European options in Black-Scholes model, Merton jump diffusion model and CGMY Levy model, all with Markov regime switching. Numerical results illustrate that although the convergence rate of method modified Fourier-Cosine expansions is slower than that of Fourier-Cosine expansions, accuracy of method of modified Fourier-Cosine expansions is greatly improved. In particular for case of CGMY Levy model, the improvement is significant.
Key words:      Levy processes    Markov regime switching    Fourier transform    Fourier Cosine extension    option pricing
收稿日期: 2015-11-05 出版日期: 2018-05-16
CLC:  O211.63  
基金资助: 国家自然科学基金重点项目(71631005); 国家自然科学基金(71471161)
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引用本文:

王春发, 陈荣达. Markov调制Levy模型定价的Fourier-Cos方法[J]. 高校应用数学学报, 2016, 31(4): 390-404.

WANG Chun-fa, CHEN Rong-da. Option pricing in Markov regime switching Levy models using Fourier-Cosine expansions. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 390-404.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2016/V31/I4/390

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