Numerical simulation of a Finite Moment Log Stable model for a European call option
 作者： H. Zhang,  F. Liu,  I. Turner,  S. Chen,  Q. Yang 作者单位： 1Fuzhou University2Queensland University of Technology3Southwestern University of Finance and Economics4Shandong University 刊名： Numerical Algorithms, 2017, Vol.75 (3), pp.569-585 来源数据库： Springer Nature Journal DOI： 10.1007/s11075-016-0212-x 关键词： The FMLS model;  Riemann-Liouville fractional derivative;  Numerical simulation;  Fast Fourier transform;  Bi-conjugrate gradient stabilized method;  European option; 英文摘要： Compared to the classical Black-Scholes model for pricing options, the Finite Moment Log Stable (FMLS) model can more accurately capture the dynamics of the stock prices including large movements or jumps over small time steps. In this paper, the FMLS model is written as a fractional partial differential equation and we will present a new numerical scheme for solving this model. We construct an implicit numerical scheme with second order accuracy for the FMLS and consider the stability and convergence of the scheme. In order to reduce the storage space and computational cost, we use a fast bi-conjugate gradient stabilized method (FBi-CGSTAB) to solve the discrete scheme. A numerical example is presented to show the efficiency of the numerical method and to demonstrate the order of... convergence of the implicit numerical scheme. Finally, as an application, we use the above numerical technique to price a European call option. Furthermore, by comparing the FMLS model with the classical B-S model, the characteristics of the FMLS model are also analyzed. 原始语种摘要： Compared to the classical Black-Scholes model for pricing options, the Finite Moment Log Stable (FMLS) model can more accurately capture the dynamics of the stock prices including large movements or jumps over small time steps. In this paper, the FMLS model is written as a fractional partial differential equation and we will present a new numerical scheme for solving this model. We construct an implicit numerical scheme with second order accuracy for the FMLS and consider the stability and convergence of the scheme. In order to reduce the storage space and computational cost, we use a fast bi-conjugate gradient stabilized method (FBi-CGSTAB) to solve the discrete scheme. A numerical example is presented to show the efficiency of the numerical method and to demonstrate the order of... convergence of the implicit numerical scheme. Finally, as an application, we use the above numerical technique to price a European call option. Furthermore, by comparing the FMLS model with the classical B-S model, the characteristics of the FMLS model are also analyzed.

• option　选择
• model　模型
• European　欧洲人
• prices　行情
• implicit　隐含的
• pricing　定价
• simulation　模拟
• stock　岩株
• Black　布莱克
• numerical　数字的