In this paper, three compact finite difference schemes on uniform mesh to solve the fractional Black-Scholes partial differential equation for European type option are presented. The time-fractional derivative is approximated by $L1 $ formula, $L1-2$ formula and $L2-1_{\sigma }$ formula respectively, and three compact difference schemes with orders $O((\Delta t)^{2-\alpha} +(\Delta x)^4),~ O((\Delta t)^{3-\alpha} +(\Delta x)^4)$ and $O((\Delta t)^2 + (\Delta x)^4)$ are constructed. The stability and convergence analysis of the proposed method is also analyzed. Finally, a numerical example is carried out to verify the accuracy and effectiveness of the proposed methods, and the comparisons of these schemes are given. The paper also provides numerical studies including the effect of fractional orders and the effect of different parameters on option price in the time-fractional framework.
Tarei, S. , Kanaujiya, A. and Mohapatra, J. (2025). Efficient Numerical Method for Pricing Option with Underlying Asset Follows a Fractal Stochastic Process. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.64013.2879
MLA
Tarei, S. , , Kanaujiya, A. , and Mohapatra, J. . "Efficient Numerical Method for Pricing Option with Underlying Asset Follows a Fractal Stochastic Process", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.64013.2879
HARVARD
Tarei, S., Kanaujiya, A., Mohapatra, J. (2025). 'Efficient Numerical Method for Pricing Option with Underlying Asset Follows a Fractal Stochastic Process', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.64013.2879
CHICAGO
S. Tarei , A. Kanaujiya and J. Mohapatra, "Efficient Numerical Method for Pricing Option with Underlying Asset Follows a Fractal Stochastic Process," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.64013.2879
VANCOUVER
Tarei, S., Kanaujiya, A., Mohapatra, J. Efficient Numerical Method for Pricing Option with Underlying Asset Follows a Fractal Stochastic Process. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.64013.2879
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