Results 1 to 10 of about 228 (169)
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Black–Scholes option pricing equations described by the Caputo generalized fractional derivative
Chaos, Solitons & Fractals, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fall, Aliou Niang +2 more
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A space-time spectral method for time-fractional Black-Scholes equation
Applied Numerical Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
An, Xingyu +4 more
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Fractional Fokker-Planck Equation and Black-Scholes Formula in Composite-Diffusive Regime
Journal of Statistical Physics, 2011The authors consider a generalization of the Black-Scholes model driven by anomalous diffusion. In particular, they consider what they call a composite-diffusive fractional Brownian motion driven by anomalous diffusion as a model of asset prices and discuss the corresponding fractional Fokker-Planck equation and Black-Scholes formula.
Liang, Jin-Rong +5 more
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A novel numerical scheme for a time fractional Black–Scholes equation
Journal of Applied Mathematics and Computing, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mianfu She +3 more
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Fractional model and solution for the Black‐Scholes equation
Mathematical Methods in the Applied Sciences, 2017This work presents a new model of the fractional Black‐Scholes equation by using the right fractional derivatives to model the terminal value problem. Through nondimensionalization and variable replacements, we convert the terminal value problem into an initial value problem for a fractional convection diffusion equation.
Jun‐Sheng Duan +3 more
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2021
Summary: In this paper, the temporal fractional Black-Scholes model (TFBSM) is discussed in the limited specific domain which the time derivative of this template is the Caputo fractional function. The value variance of the associated fractal transmission method was applied to forecast TFBSM.
Aghdam, Yones Esmaeelzade +2 more
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Summary: In this paper, the temporal fractional Black-Scholes model (TFBSM) is discussed in the limited specific domain which the time derivative of this template is the Caputo fractional function. The value variance of the associated fractal transmission method was applied to forecast TFBSM.
Aghdam, Yones Esmaeelzade +2 more
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Multiscale estimation of processes related to the fractional Black-Scholes equation
Computational Statistics, 2003The authors propose the following model for the log-price: \(R_\alpha(t)=D_t^\alpha X_t=\sigma_t D_t^\alpha B(\lambda(t))\), where \(D_t^\alpha\) is the Riemann-Liouville fractional derivative of order \(\alpha\), \(B\) is the classical Brownian motion, and \(\sigma_t\), \(\lambda\) are some nonrandom functions.
Ricardo Fernández-Pascual +2 more
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Fractional Black–Scholes equation
International Journal of Financial Engineering, 2017In 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–
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A 2nd-Order FDM for a 2D Fractional Black-Scholes Equation
2017We develop a finite difference method (FDM) for a 2D fractional Black-Scholes equation arising in the optimal control problem of pricing European options on two assets under two independent geometric Levy processes. We establish the convergence of the method by showing that the FDM is consistent, stable and monotone.
Wen Chen 0014, Song Wang 0004
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An efficient wavelet method for the time‐fractional Black–Scholes equations
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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