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Applications of Fourier Transform to Smile Modeling

Theory and Implementation

  • Book
  • © 2010

Overview

Authors:
  1. Jianwei Zhu

    1. Lucht Probst Associates GmbH, Frankfurt, Germany

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Part of the book series: Springer Finance (FINANCE)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XV
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  2. Option Valuation and the Volatility Smile

    • Jianwei Zhu
    Pages 1-19

  3. Characteristic Functions in Option Pricing

    • Jianwei Zhu
    Pages 21-43

  4. Stochastic Volatility Models

    • Jianwei Zhu
    Pages 45-76

  5. Numerical Issues of Stochastic Volatility Models

    • Jianwei Zhu
    Pages 77-111

  6. Simulating Stochastic Volatility Models

    • Jianwei Zhu
    Pages 113-133

  7. Stochastic Interest Models

    • Jianwei Zhu
    Pages 135-152

  8. Poisson Jumps

    • Jianwei Zhu
    Pages 153-172

  9. Lévy Jumps

    • Jianwei Zhu
    Pages 173-202

  10. Integrating Various Stochastic Factors

    • Jianwei Zhu
    Pages 203-221

  11. Exotic Options with Stochastic Volatilities

    • Jianwei Zhu
    Pages 223-271

  12. Libor Market Model with Stochastic Volatilities

    • Jianwei Zhu
    Pages 273-317

  13. Back Matter

    Pages 319-330
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Keywords

About this book

This book addresses the applications of Fourier transform to smile modeling. Smile effect is used generically by ?nancial engineers and risk managers to refer to the inconsistences of quoted implied volatilities in ?nancial markets, or more mat- matically, to the leptokurtic distributions of ?nancial assets and indices. Therefore, a sound modeling of smile effect is the central challenge in quantitative ?nance. Since more than one decade, Fourier transform has triggered a technical revolution in option pricing theory. Almost all new developed option pricing models, es- cially in connection with stochastic volatility and random jump, have extensively applied Fourier transform and the corresponding inverse transform to express - tion pricing formulas. The large accommodation of the Fourier transform allows for a very convenient modeling with a general class of stochastic processes and d- tributions. This book is then intended to present a comprehensive treatment of the Fourier transform in the option valuation, covering the most stochastic factors such as stochastic volatilities and interest rates, Poisson and Levy ´ jumps, including some asset classes such as equity, FX and interest rates, and providing numerical ex- ples and prototype programming codes. I hope that readers will bene?t from this book not only by gaining an overview of the advanced theory and the vast large l- erature on these topics, but also by gaining a ?rst-hand feedback from the practice on the applications and implementations of the theory.

Reviews

From the reviews of the second edition:

“The book is intended to present a comprehensive treatment of the Fourier transform in option pricing … . It is aimed to graduate students and researchers looking for a compact introduction to smile modeling with Fourier transform, or to financial engineers and risk managers working on option pricing and willing to implement models with characteristic functions. … a self-contained style, presenting the basic concepts of option pricing theory and the advanced techniques of asset modeling, especially with respect to Fourier transform and characteristic functions.” (Iulian Stoleriu, Zentralblatt MATH, Vol. 1182, 2010)

Authors and Affiliations

  • Lucht Probst Associates GmbH, Frankfurt, Germany

    Jianwei Zhu

Bibliographic Information

  • Book Title: Applications of Fourier Transform to Smile Modeling

  • Book Subtitle: Theory and Implementation

  • Authors: Jianwei Zhu

  • Series Title: Springer Finance

  • DOI: https://doi.org/10.1007/978-3-642-01808-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2010

  • Hardcover ISBN: 978-3-642-01807-7Published: 16 October 2009

  • Softcover ISBN: 978-3-642-26094-0Published: 14 March 2012

  • eBook ISBN: 978-3-642-01808-4Published: 03 October 2009

  • Series ISSN: 1616-0533

  • Series E-ISSN: 2195-0687

  • Edition Number: 2

  • Number of Pages: XV, 330

  • Number of Illustrations: 7 b/w illustrations

  • Additional Information: Originally published as volume 493 in the series: Lecture Notes in Economics and Mathematical Systems

  • Topics: Business Mathematics, Finance, general, Quantitative Finance

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