An improved approximate method for solving two-dimensional time-fractional-order Black-Scholes model: a finite difference approach
Copyright policy )An improved approximate method for solving two-dimensional time-fractional-order Black-Scholes model: a finite difference approach
<abstract><p>In this paper, we considered the two-dimensional fractional-order Black-Scholes model in the Liouville-Caputo sense. The Black-Scholes model was an important tool in the financial market, used for determining option prices in the European-style market. However, finding a closed-form analytical solution for the fractional-order partial differential equation was challenging. To address this, we introduced an improved finite difference method for approximating the solution of the two-dimensional fractional-order Black-Scholes model in the Liouville-Caputo sense, based on the Crank-Nicolson finite difference method. This method combined the concepts of the finite difference method for solving the multidimensional Black-Scholes model and the finite difference method for solving the fractional-order heat equation. We analyzed the conditional stability and the order of convergence. Furthermore, numerical examples were provided to illustrate the determination of option prices.</p></abstract>
- Mahasarakham University Thailand
- Khon Kaen University Thailand
Finite difference, Economics, Fractional Order Control, Mathematical analysis, Convergence Analysis of Iterative Methods for Nonlinear Equations, FOS: Economics and business, Higher-Order Methods, Engineering, Black–Scholes model, multi-dimensional model, QA1-939, FOS: Mathematics, Econometrics, finite difference method, Anomalous Diffusion Modeling and Analysis, Order (exchange), Analysis and Design of Fractional Order Control Systems, Volatility (finance), Numerical Analysis, Time-Fractional Diffusion Equation, Derivative-Free Methods, Applied mathematics, Fractional Derivatives, Control and Systems Engineering, numerical simulation, Modeling and Simulation, Physical Sciences, crank-nicolson, time fracional-order black-scholes model, Mathematics, Finance
Finite difference, Economics, Fractional Order Control, Mathematical analysis, Convergence Analysis of Iterative Methods for Nonlinear Equations, FOS: Economics and business, Higher-Order Methods, Engineering, Black–Scholes model, multi-dimensional model, QA1-939, FOS: Mathematics, Econometrics, finite difference method, Anomalous Diffusion Modeling and Analysis, Order (exchange), Analysis and Design of Fractional Order Control Systems, Volatility (finance), Numerical Analysis, Time-Fractional Diffusion Equation, Derivative-Free Methods, Applied mathematics, Fractional Derivatives, Control and Systems Engineering, numerical simulation, Modeling and Simulation, Physical Sciences, crank-nicolson, time fracional-order black-scholes model, Mathematics, Finance
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