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Saddlepoint Approximation Methods in Financial Engineering

  • Book
  • © 2018

Overview

Authors:
  1. Yue Kuen Kwok

    1. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Wendong Zheng

    1. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Illustrative examples help readers to assess the saddlepoint approximation formulas in various contexts
  • Appendices provide the background analytic tools used, making the book self-contained
  • Well suited as a textbook for university courses in financial mathematics
  • Serves to popularize the use of the saddlepoint approximation approach to deriving reliable analytic approximation formulas

Part of the book series: SpringerBriefs in Quantitative Finance (BRIEFFINANCE)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Cumulant Generating Functions and Steepest Descent Method

    • Yue Kuen Kwok, Wendong Zheng
    Pages 1-9

  3. Saddlepoint Approximations to Density Functions, Tail Probabilities and Tail Expectations

    • Yue Kuen Kwok, Wendong Zheng
    Pages 11-55

  4. Extended Saddlepoint Approximation Methods

    • Yue Kuen Kwok, Wendong Zheng
    Pages 57-71

  5. Saddlepoint Approximation Formulas for Pricing Options

    • Yue Kuen Kwok, Wendong Zheng
    Pages 73-95

  6. Saddlepoint Approximation for Credit Portfolios

    • Yue Kuen Kwok, Wendong Zheng
    Pages 97-122

  7. Back Matter

    Pages 123-128
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Keywords

About this book

This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. 

The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results.

Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities ofthe topic. It will also be valuable to quantitative analysts in financial institutions who strive for effective valuation of prices of exotic financial derivatives and risk positions of portfolios of risky instruments.

 

Authors and Affiliations

  • Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China

    Yue Kuen Kwok, Wendong Zheng

Bibliographic Information

  • Book Title: Saddlepoint Approximation Methods in Financial Engineering

  • Authors: Yue Kuen Kwok, Wendong Zheng

  • Series Title: SpringerBriefs in Quantitative Finance

  • DOI: https://doi.org/10.1007/978-3-319-74101-7

  • Publisher: Springer Cham

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

  • Copyright Information: The Author(s) 2018

  • Softcover ISBN: 978-3-319-74100-0Published: 27 February 2018

  • eBook ISBN: 978-3-319-74101-7Published: 16 February 2018

  • Series ISSN: 2192-7006

  • Series E-ISSN: 2192-7014

  • Edition Number: 1

  • Number of Pages: X, 128

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Quantitative Finance

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