Numerical Algorithms

, Volume 75, Issue 3, pp 569–585

# Numerical simulation of a Finite Moment Log Stable model for a European call option

Original Paper

## Abstract

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.

### Keywords

The FMLS model Riemann-Liouville fractional derivative Numerical simulation Fast Fourier transform Bi-conjugrate gradient stabilized method European option

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## Authors and Affiliations

• H. Zhang
• 1
• F. Liu
• 2
• I. Turner
• 2
• S. Chen
• 3
• 4
• Q. Yang
• 2
1. 1.School of Mathematical and Computer SciencesFuzhou UniversityFuzhouChina
2. 2.School of Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia
3. 3.School of Economic MathematicsSouthwestern University of Finance and EconomicsChengduChina
4. 4.School of MathematicsShandong UniversityJinanChina