Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model [PDF]
MathematicsIn this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to ...
Xiaoying Jiang, Chunmei Shi, Yujie Wei
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A Fast Computational Scheme for Solving the Temporal-Fractional Black–Scholes Partial Differential Equation [PDF]
Fractal and Fractional, 2023 In this work, we propose a fast scheme based on higher order discretizations on graded meshes for resolving the temporal-fractional partial differential equation (PDE), which benefits the memory feature of fractional calculus.
Rouhollah Ghabaei +3 more
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Nonlinear Engineering, 2016 In this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation.
Ravi Kanth A.S.V., Aruna K.
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Optimal approximations for the free boundary problems of the space-time fractional Black-Scholes equations using a combined physics-informed neural network. [PDF]
Sci RepSong L, Tan Y, Yu F, Luo Y, Zheng J.
europepmc +3 more sources
A hybrid Chelyshkov wavelet-finite differences method for time-fractional black-Scholes equation [PDF]
Journal of Mahani Mathematical ResearchIn this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization.
Seyyed Amjad Samareh Hashemi +2 more
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The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method [PDF]
Advances in Mathematical Physics, 2020 In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process.
Naravadee Nualsaard +2 more
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Review of the Fractional Black-Scholes Equations and Their Solution Techniques
Fractal and FractionalThe pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of
Hongmei Zhang +3 more
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A class of intrinsic parallel difference methods for time-space fractional Black–Scholes equation
Advances in Difference Equations, 2018 To quickly solve the fractional Black–Scholes (B–S) equation in the option pricing problems, in this paper, we construct pure alternative segment explicit–implicit (PASE-I) and pure alternative segment implicit–explicit (PASI-E) difference schemes for ...
Yue Li, Xiaozhong Yang, Shuzhen Sun
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Fractional Black–Scholes equation [PDF]
International Journal of Financial Engineering, 2017 In this paper, it has been shown that the combined use of exponential operators and special functions provides a powerful tool to solve certain class of generalized space fractional Laguerre heat equation. It is shown that exponential operators are powerful and effective method for solving certain singular integral equations and space fractional Black–
Arman Aghili
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An efficient wavelet method for the time‐fractional Black–Scholes equations [PDF]
Mathematical Methods in the Applied SciencesA European option is one of the common types of options in financial markets, which can be modeled by a time‐fractional parabolic PDE, known as the time‐fractional Black–Scholes equation (BSE). In this article, we propose an effective numerical scheme by applying Müntz–Legendre wavelets (MLW) for the solution of the given BSE.
Boonrod Yuttanan +2 more
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