Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 71, Issue 9, Pages 1772-1783Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2016.02.007
Keywords
Time fractional Black-Scholes model; Modified Riemann-Liouville fractional derivative; Caputo fractional derivative; European option; Numerical simulation
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Funding
- National NSF of China [11201077, 11301194]
- China Scholarship Fund
- science and technology development fund of Fuzhou University [2014-XQ-27]
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When considering the price change of the underlying fractal transmission system, a fractional Black-Scholes(B-S) model with an alpha-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-alpha 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. (C) 2016 Elsevier Ltd. All rights reserved.
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