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Fractional model and solution for the Black‐Scholes equation
Author(s) -
Duan JunSheng,
Lu Lei,
Chen Lian,
An YuLian
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4638
Subject(s) - mathematics , laplace transform , work (physics) , initial value problem , variable (mathematics) , terminal (telecommunication) , fractional calculus , black–scholes model , fourier transform , laplace's equation , mathematical analysis , anomalous diffusion , diffusion , partial differential equation , thermodynamics , computer science , econometrics , volatility (finance) , telecommunications , knowledge management , physics , innovation diffusion
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.