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Modular Pricing of Options

An Application of Fourier Analysis

  • Jianwei Zhu

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 493)

Table of contents

  1. Front Matter
    Pages i-x
  2. Jianwei Zhu
    Pages 1-23
  3. Jianwei Zhu
    Pages 25-97
  4. Jianwei Zhu
    Pages 99-155
  5. Jianwei Zhu
    Pages 157-160
  6. Back Matter
    Pages 161-174

About this book

Introduction

From a technical point of view, the celebrated Black and Scholes option pricing formula was originally developed using a separation of variables technique. However, already Merton mentioned in his seminal 1973 pa­ per, that it could have been developed by using Fourier transforms as well. Indeed, as is well known nowadays, Fourier transforms are a rather convenient solution technique for many models involving the fundamental partial differential equation of financial economics. It took the community nearly another twenty years to recognize that Fourier transform is even more useful, if one applies it to problems in financial economics without seeking an explicit analytical inverse trans­ form. Heston (1993) probably was the first to demonstrate how to solve a stochastic volatility option pricing model quasi analytically using the characteristic function of the problem, which is nothing else than the Fourier transform of the underlying Arrow /Debreu-prices, and doing the inverse transformation numerically. This opened the door for a whole bunch of new closed form solutions in the transformed Fourier space and still is one of the most active research areas in financial economics.

Keywords

Finanzierungstheorie Fourier analysis Fourieranalyse Option pricing Optionspreise Random jumps Stochastic Interest Rates Stochastic interest rate Stochastic volatility calculus function modeling

Authors and affiliations

  • Jianwei Zhu
    • 1
  1. 1.Wirtschaftswissenschaftliche FakultätEberhard-Karls-Universität TübingenTübingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04309-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-67916-5
  • Online ISBN 978-3-662-04309-7
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site
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