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© 2011

PDE and Martingale Methods in Option Pricing

Benefits

  • Unified and detailed treatment of PDE and martingale methods in option pricing

  • Full treatment of arbitrage theory in discrete and continuous time

  • Self-contained introduction to advanced methods (Malliavin calculus, Levy processes, Fourier methods, etc)

Textbook

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

  1. 1.Department of MathematicsUniversity of BolognaBologna

About the authors

Andrea Pascucci is Professor of Mathematics at the University of Bologna where he is director of a master program in Quantitative Finance. His research interests include second order parabolic partial differential equations and stochastic analysis with applications to finance (pricing of European, American and Asian options).

Bibliographic information

Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

“The author provides an excellent overview of methods from the theory of partial differential equations and stochastic processes used in mathematical finance. … The book is well written, the mathematical level is quite sophisticated and a broad range of material is covered. At the same time, there is a clear focus on applications. The book is therefore warmly recommended for graduate students as well as for professionals in the financial industry.” (Johan Tysk, Mathematical Reviews, Issue 2012 i)

“The book is written for graduate and advanced undergraduate students and gives an introduction to the modern theory of option pricing. … this book covers a wide range of topics with good motivations on a rigorous mathematical level.” (Sören Christensen, Zentralblatt MATH, Vol. 1214, 2011)