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Large Deviations and Asymptotic Methods in Finance pp 345–411Cite as

Asymptotic Expansion Approach in Finance

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 110))

Abstract

This paper provides a survey on an asymptotic expansion approach to valuation and hedging problems in finance. The asymptotic expansion is a widely applicable methodology for analytical approximations of expectations of certain Wiener functionals. Hence not only academic researchers but also practitioners have been applying the scheme to a variety of problems in finance such as pricing and hedging derivatives under high-dimensional stochastic environments. The present note gives an overview of the approach.

I dedicate this note to the late Professor Peter Laurence and Koji Takahashi.

I am very grateful to Professor Fujii, Professor Shiraya, Professor Takehara, Dr. Toda, Dr. Tsuzuki and Professor Yamada, my coauthors in the original articles, which are main bases for this survey.

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  1. Graduate School of Economics, The University of Tokyo, 7-3-1, Hongo, Tokyo, Bunkyo-ku, 113-0033, Japan

    Akihiko Takahashi

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  1. Akihiko Takahashi
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  1. Technische Universität Berlin, Institut für Mathematik, Weierstraß- Institut für Angewandte Analysis und Stochastik, Berlin, Germany

    Peter K. Friz

  2. Department of Mathematics, City University of New York Baruch College, New York, New York, USA

    Jim Gatheral

  3. Department of Mathematics, Ohio University, Athens, Ohio, USA

    Archil Gulisashvili

  4. Department of Mathematics, Imperial College London, London, United Kingdom

    Antoine Jacquier

  5. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Josef Teichmann

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Takahashi, A. (2015). Asymptotic Expansion Approach in Finance. In: Friz, P., Gatheral, J., Gulisashvili, A., Jacquier, A., Teichmann, J. (eds) Large Deviations and Asymptotic Methods in Finance. Springer Proceedings in Mathematics & Statistics, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-11605-1_13

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