Please wait a minute...
高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (4): 390-404    DOI:
    
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
Download:   PDF(0KB)
Export: BibTeX | EndNote (RIS)      

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     
Received: 05 November 2015      Published: 16 May 2018
CLC:  O211.63  
  F830.91  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
WANG Chun-fa
CHEN Rong-da
Cite this article:

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.

URL:

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


Markov调制Levy模型定价的Fourier-Cos方法

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 
[1] LIU Jiang, ZHANG Long, JIANG Zhong-chuan, LI Yan-qing. Synchronous control on inverter system of grid connected high-power wind generators with nonlinear and pulse disturbance#br#[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 388-402.
[2] BAI Yong-xin, TIAN Mao-zai. Confidence interval construction for the risk difference of chronic disease based on saddle-point approximation under poisson distribution[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 253-266.
[3] WU Xiu-feng, HUANG Jun-jie, Alatancang. Pertubation of four classes of point spectra for $3\times3$ upper triangular operator matrices[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 93-102.
[4] KONG Xiang-shan, LI Hai-tao, ZHAO Hong-xin, LV Xun-jing. Bifurcation of positive solutions for a class of integral boundary value problems of fractional differential equations[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 13-22.
[5] CHEN Xiao-li, HU Qiao-zhen. Endpoint estimates for commutators of intrinsic square functions on the weighted weak Hardy spaces[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 109-119.