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Automatic Differentiation for Computational Finance

- incollection -
 

Area
Finance

Author(s)
C. H. Bischof , H. M. Bücker , B. Lang

Published in
Computational Methods in Decision-Making, Economics and Finance

Editor(s)
E. J. Kontoghiorghes, B. Rustem, S. Siokos

Year
2002

Publisher
Kluwer Academic Publishers

Abstract
Automatic differentiation (ad) is a powerful technique allowing to compute derivatives of a function given by a (potentially very large) piece of code. The basic principles of ad and some available tools implementing this technology are reviewed. ad is superior to divided differences because ad-generated derivative values are free of approximation errors, and superior to symbolic differentiation because code of very high complexity can be handled, in contrast to computer algebra systems whose applicability is limited to rather simple functions. In addition, the cost for computing gradients of scalar-valued functions with either divided differences or symbolic differentiation grows linearly with the number of variables, whereas the so-called reverse mode of ad can compute such gradients at constant cost.

AD Theory and Techniques
Introduction

BibTeX
@INCOLLECTION{
         Bischof2002ADf,
       author = "C. H. Bischof and H. M. B{\"u}cker and B. Lang",
       title = "Automatic Differentiation for Computational Finance",
       booktitle = "Computational Methods in Decision-Making, Economics and Finance",
       publisher = "Kluwer Academic Publishers",
       editor = "E. J. Kontoghiorghes and B. Rustem and S. Siokos",
       pages = "297--310",
       address = "Dordrecht",
       series = "Applied Optimization",
       abstract = "Automatic differentiation (AD) is a powerful technique allowing to compute
         derivatives of a function given by a (potentially very large) piece of code. The basic principles of
         AD and some available tools implementing this technology are reviewed. AD is superior to divided
         differences because AD-generated derivative values are free of approximation errors, and superior to
         symbolic differentiation because code of very high complexity can be handled, in contrast to
         computer algebra systems whose applicability is limited to rather simple functions. In addition, the
         cost for computing gradients of scalar-valued functions with either divided differences or symbolic
         differentiation grows linearly with the number of variables, whereas the so-called reverse mode of
         AD can compute such gradients at constant cost.",
       ad_area = "Finance",
       ad_theotech = "Introduction",
       year = "2002",
       volume = "74",
       chapter = "15",
       doi = "10.1007/978-1-4757-3613-7_15"
}


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