Recovering the local volatility in Black-Scholes model by numerical differentiation

In this article, a numerical method for recovering the local volatility in Black-Scholes model is proposed based on the Dupire formula in which the numerical derivatives are used. By Tikhonov regularization, a new numerical differentiation method in two-dimensional (2-D) case is presented. The conve...

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Bibliographic Details
Published inApplicable analysis Vol. 85; no. 6-7; pp. 681 - 692
Main Authors Yin, Binbin, Ye, Yuzhang
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.06.2006
Subjects
AMS Subject Classifications: 65M32
Black-Scholes model
Dupire formula
Local volatility
Numerical differentiation
Tikhonov regularization
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ISSN0003-6811
1563-504X
DOI10.1080/00036810500475025

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Summary:In this article, a numerical method for recovering the local volatility in Black-Scholes model is proposed based on the Dupire formula in which the numerical derivatives are used. By Tikhonov regularization, a new numerical differentiation method in two-dimensional (2-D) case is presented. The convergent analysis and numerical examples are also given. It shows that our method is efficient and stable.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036810500475025