A Fast Numerical Method for the Black-Scholes Equation of American Options

Houde Han; Xiaonan Wu

doi:10.1137/S0036142901390238

A Fast Numerical Method for the Black-Scholes Equation of American Options

Houde Han, Xiaonan Wu

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

80 Citations (Scopus)

95 Downloads (Pure)

Abstract

This paper introduces a fast numerical method for computing American option pricing problems governed by the Black-Scholes equation. The treatment of the free boundary is based on some properties of the solution of the Black-Scholes equation. An artificial boundary condition is also used at the other end of the domain. The finite difference method is used to solve the resulting problem. Computational results are given for some American call option problems. The results show that the new treatment is very efficient and gives better accuracy than the normal finite difference method.

Original language	English
Pages (from-to)	2081-2095
Number of pages	15
Journal	SIAM Journal on Numerical Analysis
Volume	41
Issue number	6
DOIs	https://doi.org/10.1137/S0036142901390238
Publication status	Published - Nov 2003

Scopus Subject Areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

User-Defined Keywords

American option
Artificial boundary condition
Finite difference method
Free boundary

Access to Document

10.1137/S0036142901390238

Full TextFinal published version, 208 KB

Cite this

@article{9419811e0dd84f27a6472941412ead3e,

title = "A Fast Numerical Method for the Black-Scholes Equation of American Options",

abstract = "This paper introduces a fast numerical method for computing American option pricing problems governed by the Black-Scholes equation. The treatment of the free boundary is based on some properties of the solution of the Black-Scholes equation. An artificial boundary condition is also used at the other end of the domain. The finite difference method is used to solve the resulting problem. Computational results are given for some American call option problems. The results show that the new treatment is very efficient and gives better accuracy than the normal finite difference method.",

keywords = "American option, Artificial boundary condition, Finite difference method, Free boundary",

author = "Houde Han and Xiaonan Wu",

note = "Funding information: Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China (hhan@ math.tsinghua.edu.cn). This research was supported in part by the Special Funds for Major State Basic Research Projects of China. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong ([email protected]). This research was supported in part by RGC of Hong Kong and FRG of Hong Kong Baptist University. Publisher copyright: Copyright {\textcopyright} 2003 Society for Industrial and Applied Mathematics",

year = "2003",

month = nov,

doi = "10.1137/S0036142901390238",

language = "English",

volume = "41",

pages = "2081--2095",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "6",

}

TY - JOUR

T1 - A Fast Numerical Method for the Black-Scholes Equation of American Options

AU - Han, Houde

AU - Wu, Xiaonan

N1 - Funding information: Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China (hhan@ math.tsinghua.edu.cn). This research was supported in part by the Special Funds for Major State Basic Research Projects of China. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong ([email protected]). This research was supported in part by RGC of Hong Kong and FRG of Hong Kong Baptist University. Publisher copyright: Copyright © 2003 Society for Industrial and Applied Mathematics

PY - 2003/11

Y1 - 2003/11

N2 - This paper introduces a fast numerical method for computing American option pricing problems governed by the Black-Scholes equation. The treatment of the free boundary is based on some properties of the solution of the Black-Scholes equation. An artificial boundary condition is also used at the other end of the domain. The finite difference method is used to solve the resulting problem. Computational results are given for some American call option problems. The results show that the new treatment is very efficient and gives better accuracy than the normal finite difference method.

AB - This paper introduces a fast numerical method for computing American option pricing problems governed by the Black-Scholes equation. The treatment of the free boundary is based on some properties of the solution of the Black-Scholes equation. An artificial boundary condition is also used at the other end of the domain. The finite difference method is used to solve the resulting problem. Computational results are given for some American call option problems. The results show that the new treatment is very efficient and gives better accuracy than the normal finite difference method.

KW - American option

KW - Artificial boundary condition

KW - Finite difference method

KW - Free boundary

UR - http://www.scopus.com/inward/record.url?scp=11044237933&partnerID=8YFLogxK

U2 - 10.1137/S0036142901390238

DO - 10.1137/S0036142901390238

M3 - Journal article

AN - SCOPUS:11044237933

SN - 0036-1429

VL - 41

SP - 2081

EP - 2095

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 6

ER -

A Fast Numerical Method for the Black-Scholes Equation of American Options

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this