Fractional model and solution for the Black‐Scholes equation
Copyright policy )Fractional model and solution for the Black‐Scholes equation
This 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. Then the problem is solved by using the Fourier‐Laplace transform. The fundamental solutions of the derived initial value problem are given and simulated and display a slow anomalous diffusion in the fractional case.
- Shanghai Institute of Technology China (People's Republic of)
asset pricing models, mathematical finance, PDEs in connection with game theory, economics, social and behavioral sciences, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Laplace transform, Black-Scholes equation, fractional derivative, initial value problem, terminal value problem, Fractional partial differential equations, Financial applications of other theories
asset pricing models, mathematical finance, PDEs in connection with game theory, economics, social and behavioral sciences, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Laplace transform, Black-Scholes equation, fractional derivative, initial value problem, terminal value problem, Fractional partial differential equations, Financial applications of other theories
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