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Modular Pricing of Options

An Application of Fourier Analysis

  • Book
  • © 2000

Overview

Authors:
  1. Jianwei Zhu

    1. Wirtschaftswissenschaftliche Fakultät, Eberhard-Karls-Universität Tübingen, Tübingen, Germany

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Jianwei Zhu
    Pages 1-23

  3. Modular Pricing of Options (MPO)

    • Jianwei Zhu
    Pages 25-97

  4. Extensions of MPO to Exotic Options

    • Jianwei Zhu
    Pages 99-155

  5. Conclusions

    • Jianwei Zhu
    Pages 157-160

  6. Back Matter

    Pages 161-174
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Keywords

About this book

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.

Authors and Affiliations

  • Wirtschaftswissenschaftliche Fakultät, Eberhard-Karls-Universität Tübingen, Tübingen, Germany

    Jianwei Zhu

Bibliographic Information

  • Book Title: Modular Pricing of Options

  • Book Subtitle: An Application of Fourier Analysis

  • Authors: Jianwei Zhu

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-662-04309-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • eBook ISBN: 978-3-662-04309-7Published: 17 April 2013

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: X, 174

  • Topics: Finance, general, Quantitative Finance

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