@Article{AAM-36-1,
author = {Zhang, Hongmei and Liu, Fawang and Shanzhen, Chen and Shen, Ming},
title = {​A Fast and High Accuracy Numerical Simulation for a Fractional Black-Scholes Model on Two Assets},
journal = {Annals of Applied Mathematics},
year = {2020},
volume = {36},
number = {1},
pages = {91--110},
abstract = {<p style="text-align: justify;">In this paper, a two dimensional (2D) fractional Black-Scholes (FBS) model
on two assets following independent geometric Lévy processes is solved numerically. A high order convergent implicit difference scheme is constructed and
detailed numerical analysis is established. The fractional derivative is a quasi-differential operator, whose nonlocal nature yields a dense lower Hessenberg
block coefficient matrix. In order to speed up calculation and save storage
space, a fast bi-conjugate gradient stabilized (FBi-CGSTAB) method is proposed to solve the resultant linear system. Finally, one example with a known
exact solution is provided to assess the effectiveness and efficiency of the presented fast numerical technique. The pricing of a European Call-on-Min option
is showed in the other example, in which the influence of fractional derivative
order and volatility on the 2D FBS model is revealed by comparing with the
classical 2D B-S model.</p>},
issn = {},
doi = {https://doi.org/2020-AAM-18094},
url = {https://global-sci.com/article/72657/a-fast-and-high-accuracy-numerical-simulation-for-a-fractional-black-scholes-model-on-two-assets}
}