PDE and Martingale Methods in Option Pricing

  • Andrea Pascucci
Part of the Bocconi & Springer Series book series (BS)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Andrea Pascucci
    Pages 1-13
  3. Andrea Pascucci
    Pages 15-96
  4. Andrea Pascucci
    Pages 97-137
  5. Andrea Pascucci
    Pages 139-166
  6. Andrea Pascucci
    Pages 167-201
  7. Andrea Pascucci
    Pages 219-256
  8. Andrea Pascucci
    Pages 275-328
  9. Andrea Pascucci
    Pages 329-387
  10. Andrea Pascucci
    Pages 389-401
  11. Andrea Pascucci
    Pages 403-428
  12. Andrea Pascucci
    Pages 429-495
  13. Andrea Pascucci
    Pages 497-540
  14. Andrea Pascucci
    Pages 541-576
  15. Andrea Pascucci
    Pages 577-597
  16. Back Matter
    Pages 599-719

About this book

Introduction

This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.

Keywords

Arbitrage theory Numerical methods in finance Option pricing Quantitative finance Stochastic calculus

Authors and affiliations

  • Andrea Pascucci
    • 1
  1. 1.Department of MathematicsUniversity of BolognaBologna

Bibliographic information

  • DOI https://doi.org/10.1007/978-88-470-1781-8
  • Copyright Information Springer Milan 2011
  • Publisher Name Springer, Milano
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-88-470-1780-1
  • Online ISBN 978-88-470-1781-8
  • Series Print ISSN 2039-1471
  • About this book