PDE and Martingale Methods in Option Pricing

2011
ISBN: 978-88-470-5627-5
Verlag: Springer Milan

Buch, Englisch, 721 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 1101 g

Reihe: Bocconi & Springer Series

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Pascucci, Andrea

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Wirtschaftswissenschaften Volkswirtschaftslehre Internationale Wirtschaft Internationale Finanzmärkte
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Anlagen & Wertpapiere
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Internationale Finanzmärkte

Über Autor(innen)

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).