Numerical solution of the time fractional Black–Scholes model governing European options. (May 2016)

• Record Type: Journal Article
• Authors: Zhang, H.; Liu, F.; Turner, I.; Yang, Q.
• Is Part Of: Computers & mathematics with applications. Volume 71:issue 9(2016)
• Page Start: 1772
• Page End: 1783
• Publication Date: 2016-05
• Subjects: Time fractional Black–Scholes model -- Modified Riemann–Liouville fractional derivative -- Caputo fractional derivative -- European option -- Numerical simulation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.02.007
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: When considering the price change of the underlying fractal transmission system, a fractional Black–Scholes(B-S) model with an α -order time fractional derivative is derived. In this paper, we discuss the numerical simulation of this time fractional Black–Scholes model (TFBSM) governing European options. A discrete implicit numerical scheme with a spatially second-order accuracy and a temporally 2 − α order accuracy is constructed. Then, the stability and convergence of the proposed numerical scheme are analyzed using Fourier analysis. Some numerical examples are chosen in order to demonstrate the accuracy and effectiveness of the proposed method. Finally, as an application, we use the TFBSM and the above numerical technique to price several different European options.