A Modified Explicit Method for the Black-Scholes Equation with Positivity Preserving Property

被引：0

作者：

Khalsaraei, M. Mehdizadeh ^{[1
]}

Jahandizi, R. Shokri ^{[1
]}

机构：

[1] Univ Maragheh, Fac Math Sci, Maragheh, Iran

来源：

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS | 2015年 / 15卷 / 04期

关键词：

Black-Scholes equation; Nonstandard finite differences; Positivity preserving; Stability;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show that the standard finite difference scheme can generate numerical drawbacks such as spurious oscillations in the solution of the famous Black-Scholes partial differential equation, in the presence of discontinuities. We propose a modification of this scheme based on a nonstandard discretization. The proposed scheme is free of spurious oscillations and satisfies the positivity requirement, as is demanded for the financial solution of the Black-Scholes equation.

引用

页码：287 / 293

页数：7

共 11 条

[1] Ames WF., 1992, NUMER METH PART D E
[2] An unconditionally positivity preserving scheme for advection-diffusion reaction equations
Chen-Charpentier, Benito M.
Kojouharov, Hristo V.
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2013, 57 (9-10) : 2177 - 2185
[3] An improvement on the positivity results for 2-stage explicit Runge-Kutta methods
Khalsaraei, M. Mehdizadeh
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 235 (01) : 137 - 143
[4] Khalsaraei MM, 2014, SAHAND COMMUN MATH A, V1, P47
[5] Khodadoosti F., COMPUTATION IN PRESS
[6] Mehdizadeh Khalsaraei M., 2014, COMPUTATIONAL METHOD, V2, P85
[7] Mickens R.E., 1993, NONSTANDARD FINITE D
[8] Milev M., 2010, SERDICA MATH J, V36, P75
[9] Efficient implicit scheme with positivity preserving and smoothing properties
Milev, Mariyan
Tagliani, Aldo
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 243 : 1 - 9
[10] Numerical valuation of discrete double barrier options
Milev, Mariyan
Tagliani, Aldo
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 233 (10) : 2468 - 2480

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