Name
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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s11075-016-0212-x | Numerical Algorithms |
Keywords | Field | DocType |
The FMLS model,Riemann-Liouville fractional derivative,Numerical simulation,Fast Fourier transform,Bi-conjugrate gradient stabilized method,European option | Convergence (routing),Numerical technique,Mathematical optimization,Computer simulation,Mathematical analysis,Fast Fourier transform,Rate of convergence,Numerical analysis,Call option,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
75 | 3 | 1017-1398 |
Citations | PageRank | References |
1 | 0.39 | 4 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| H. Zhang | 1 | 1 | 0.72 |
| F. Liu | 2 | 419 | 42.86 |
| Ian Turner | 3 | 1016 | 122.29 |
| Shanzhen Chen | 4 | 10 | 2.32 |
| Qianqian Yang | 5 | 152 | 10.71 |