Fractional model and solution for the Black-Scholes equation

被引：20
|
作者：
Duan, Jun-Sheng [1 ]
Lu, Lei [1 ]
Chen, Lian [1 ]
An, Yu-Lian [1 ]
机构：
[1] Shanghai Inst Technol, Sch Sci, Shanghai 201418, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 02期
基金：
中国国家自然科学基金; 上海市自然科学基金;
关键词：
asset pricing models; Black-Scholes equation; fractional derivative; initial value problem; mathematical finance; terminal value problem; PARTIAL-DIFFERENTIAL-EQUATIONS;
D O I：
10.1002/mma.4638
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：697 / 704
页数：8
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