A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models

A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models

A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete...

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Main Authors: Shengwu Zhou, Wei Li, Yu Wei, Cui Wen
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/205686
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spelling doaj-393c4b737ba046adab6ca96d6ae2c76a2020-11-25T00:44:08ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/205686205686A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing ModelsShengwu Zhou0Wei Li1Yu Wei2Cui Wen3College of Sciences, China University of Mining and Technology, Jiangsu, Xuzhou 221116, ChinaCollege of Sciences, China University of Mining and Technology, Jiangsu, Xuzhou 221116, ChinaCollege of Sciences, China University of Mining and Technology, Jiangsu, Xuzhou 221116, ChinaCollege of Sciences, China University of Mining and Technology, Jiangsu, Xuzhou 221116, ChinaA positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable.http://dx.doi.org/10.1155/2012/205686
collection DOAJ
language English
format Article
sources DOAJ
author Shengwu Zhou
Wei Li
Yu Wei
Cui Wen
spellingShingle Shengwu Zhou
Wei Li
Yu Wei
Cui Wen
A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models
Journal of Applied Mathematics
author_facet Shengwu Zhou
Wei Li
Yu Wei
Cui Wen
author_sort Shengwu Zhou
title A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models
title_short A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models
title_full A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models
title_fullStr A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models
title_full_unstemmed A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models
title_sort positivity-preserving numerical scheme for nonlinear option pricing models
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable.
url http://dx.doi.org/10.1155/2012/205686
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AT shengwuzhou positivitypreservingnumericalschemefornonlinearoptionpricingmodels
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