Pseudo-Differential Operators

Pricing Derivatives Under Lévy Models

Modern Finite-Difference and Pseudo-Differential Operators Approach

Authors: Itkin, Andrey

  • Introduction of a modern finite-difference approach  
  • Presents few new results on FD schemes for PDEs, including schemes which preserve positivity  
  • Gives the reader a detailed description of the new method, including the whole theory and real practical examples so it can be immediately used for building reader's own applications
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eBook $74.99
price for USA (gross)
  • ISBN 978-1-4939-6792-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-1-4939-6790-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary.


The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method.


Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.

About the authors

Andrey Itkin is an Adjunct Professor of computational and algorithmic finance at the Tandon School of Enginering at New York University and Director, Senior Quant Research Associate at Bank of America.

Table of contents (10 chapters)

  • Basics of the Finite Difference Method

    Itkin, Andrey

    Pages 3-19

  • Modern Finite Difference Approach

    Itkin, Andrey

    Pages 21-58

  • An M-Matrix Theory and FD

    Itkin, Andrey

    Pages 59-82

  • A Brief Introduction to Lévy Processes

    Itkin, Andrey

    Pages 85-100

  • Pseudoparabolic and Fractional Equations of Option Pricing

    Itkin, Andrey

    Pages 101-134

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4939-6792-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-1-4939-6790-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Pricing Derivatives Under Lévy Models
Book Subtitle
Modern Finite-Difference and Pseudo-Differential Operators Approach
Authors
Series Title
Pseudo-Differential Operators
Series Volume
12
Copyright
2017
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media LLC
eBook ISBN
978-1-4939-6792-6
DOI
10.1007/978-1-4939-6792-6
Softcover ISBN
978-1-4939-6790-2
Series ISSN
2297-0355
Edition Number
1
Number of Pages
XX, 308
Number of Illustrations and Tables
2 b/w illustrations, 62 illustrations in colour
Topics