Springer Finance

A Benchmark Approach to Quantitative Finance

Authors: Platen, Eckhard, Heath, David

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eBook $69.99
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  • ISBN 978-3-540-47856-0
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  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-3-540-26212-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
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  • ISBN 978-3-642-06565-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

The benchmark approach provides a general framework for financial market modeling, which extends beyond the standard risk neutral pricing theory. It permits a unified treatment of portfolio optimization, derivative pricing, integrated risk management and insurance risk modeling. The existence of an equivalent risk-neutral pricing measure is not required. Instead, it leads to pricing formulae with respect to the real world probability measure. This yields important modeling freedom which turns out to be necessary for the derivation of realistic, parsimonious market models. The first part of the book describes the necessary tools from probability theory, statistics, stochastic calculus and the theory of stochastic differential equations with jumps. The second part is devoted to financial modeling under the benchmark approach. Various quantitative methods for the fair pricing and hedging of derivatives are explained. The general framework is used to provide an understanding of the nature of stochastic volatility. The book is intended for a wide audience that includes quantitative analysts, postgraduate students and practitioners in finance, economics and insurance. It aims to be a self-contained, accessible but mathematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book should stimulate interest in the benchmark approach by describing some of its power and wide applicability.

About the authors

Professor Eckhard Platen is a joint appointment between the School of Finance and Economics and the Department of Mathematical Sciences to the 1997 created Chair in Quantitative Finance at the University of Technology Sydney. Prior to this appointment he was Founding Head of the Centre for Financial Mathematics at the Institute of Advanced Studies at the Australian National University in Canberra. He completed a PhD in Mathematics at the Technical University in Dresden in 1975 and obtained in 1985 his Dr. sc. from the Academy of Sciences in Berlin, where he headed at the Weierstrass Institute the Sector of Stochastics.
He is co-author of two successful books on Numerical Methods for Stochastic Differential Equations, published by Springer Verlag, and has authored more than 100 research papers in quantitative finance and mathematics.


Dr David Heath works as a Senior Research Fellow in Quantitative Finance at the University of Technology, Sydney.  During the early 1990s he became interested in various aspects of quantitative finance.  He completed his PhD in financial mathematics at the Australian National University at the Centre for Financial Mathematics in 1995.  Since this time his main research interests have focussed on the application of advanced numerical methods for the pricing and hedging of index, equity, FX and interest rate derivatives.  These numerical methods include PDE, Monte Carlo and Markov chain methods.  He has developed a range of new quantitative methods that are specifically designed for the benchmark approach. Dr Heath has authored more than thirteen publications in financial mathematics. 

Reviews

From the reviews:

"The book under review introduces quantitative finance using the benchmark approach. … It is quite a nice blend of narrative and mathematics. There are also some bigger examples which contribute nicely to the overall presentation. … Exercises are provided at the end of each chapter. The authors even provide solutions to exercises. … I think it could be quite useful for students, because of the first part of the book, and to practitioners, due to the exposition in the second part of the book." (Ita Cirovic Donev, MathDL, March, 2007)

"This book provides an introduction to quantitative finance. … It aims to stimulate interest in the benchmark approach by describing some of its power and wide applicability. It is intended for quantitative analysts postgraduate students, practioners in finance, economics and insurance. … It is designed for three groups of users. Firstly, it provides useful information to financial analysts and practioners. Secondly, it aims to introduce those with a reasonable basic mathematical background. Thirdly, researchers may find the later parts of the book interesting … ." (Klaus Ehemann, Zentralblatt MATH, Vol. 1104 (6), 2007)

"The book is a rather comprehensive treatment of quantitative finance and distinguishes itself from other analogous treatments by using a novel approach that allows one to generalize various existing results and to some extent also allows one to bridge a certain gap between current and classical approaches. … The comprehensiveness of the book is very valuable for research … ." (Wolfgang J. Runggaldier, Mathematical Reviews, Issue 2008 d)

“A comprehensive introduction to the mathematical foundations of finance. It is thorough and encyclopedic, providing a wide range of definitions and theorems that are useful in the subject. … a valuable text for well-motivated students interested in these topics, whether they are pursuing problems within the classical framework or beyond the assumptions of the basic theory.” (Gunduz Caginalp, SIAM Review, Vol. 52 (2), 2010)


Table of contents (16 chapters)

  • Preliminaries from Probability Theory

    Platen, Eckhard (et al.)

    Pages 1-53

  • Statistical Methods

    Platen, Eckhard (et al.)

    Pages 55-98

  • Modeling via Stochastic Processes

    Platen, Eckhard (et al.)

    Pages 99-132

  • Diffusion Processes

    Platen, Eckhard (et al.)

    Pages 133-162

  • Martingales and Stochastic Integrals

    Platen, Eckhard (et al.)

    Pages 163-203

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-540-47856-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-3-540-26212-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-3-642-06565-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Benchmark Approach to Quantitative Finance
Authors
Series Title
Springer Finance
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47856-0
DOI
10.1007/978-3-540-47856-0
Hardcover ISBN
978-3-540-26212-1
Softcover ISBN
978-3-642-06565-1
Series ISSN
1616-0533
Edition Number
1
Number of Pages
XVI, 700
Number of Illustrations and Tables
199 b/w illustrations
Topics