Financial Modeling

A Backward Stochastic Differential Equations Perspective

  • Stéphane Crépey

Part of the Springer Finance book series (FINANCE)

Also part of the Springer Finance Textbooks book sub series (SFTEXT)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. An Introductory Course in Stochastic Processes

    1. Front Matter
      Pages 1-1
    2. Stéphane Crépey
      Pages 45-80
  3. Pricing Equations

    1. Front Matter
      Pages 81-81
    2. Stéphane Crépey
      Pages 83-122
    3. Stéphane Crépey
      Pages 123-155
  4. Numerical Solutions

    1. Front Matter
      Pages 157-160
    2. Stéphane Crépey
      Pages 161-197
    3. Stéphane Crépey
      Pages 199-211
    4. Stéphane Crépey
      Pages 213-241
    5. Stéphane Crépey
      Pages 243-258
  5. Applications

    1. Front Matter
      Pages 259-259
  6. Jump-Diffusion Setup with Regime Switching (∗∗)

    1. Front Matter
      Pages 321-321
    2. Stéphane Crépey
      Pages 323-358
    3. Stéphane Crépey
      Pages 359-368
    4. Stéphane Crépey
      Pages 369-387

About this book

Introduction

Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes. It also contains a review of quantitative finance tools, including Fourier techniques, Monte Carlo methods, finite differences and model calibration schemes. With a view to use in graduate courses in computational finance and financial modeling, corrected problem sets and Matlab sheets have been provided.

Stéphane Crépey’s  book starts with a few chapters on classical stochastic processes material, and then... fasten your seatbelt... the author starts traveling backwards in time through backward stochastic differential equations (BSDEs). This does not mean that one has to read the book backwards, like a manga! Rather, the possibility to move backwards in time, even if from a variety of final scenarios following a probability law, opens a multitude of possibilities for all those pricing problems whose solution is not a straightforward expectation. For example, this allows for framing problems like pricing with credit and funding costs in a rigorous mathematical setup. This is, as far as I know, the first book written for several levels of audiences, with applications to financial modeling and using BSDEs as one of the main tools, and as the song says: "it's never as good as the first time".

Damiano Brigo, Chair of Mathematical Finance, Imperial College London

While the classical theory of arbitrage free pricing has matured, and is now well understood and used by the finance industry, the theory of BSDEs continues to enjoy a rapid growth and remains a domain restricted to academic researchers and a handful of practitioners. Crépey’s book presents this novel approach to a wider community of researchers involved in mathematical modeling in finance. It is clearly an essential reference for anyone interested in the latest developments in financial mathematics.      

Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative Finance

Keywords

91G20,91G60, 91G80 backward stochastic differential equations computational finance financial modeling partial differential equations pricing and hedging

Authors and affiliations

  • Stéphane Crépey
    • 1
  1. 1.Département de mathématiques, Laboratoire d'Analyse & ProbabilitésUniversité d'Evry Val d'EssoneEvryFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-37113-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-37112-7
  • Online ISBN 978-3-642-37113-4
  • Series Print ISSN 1616-0533
  • Series Online ISSN 2195-0687
  • About this book
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