Overview
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.
Full Product Details
Author: Andrea Pascucci
Publisher: Springer Verlag
Imprint: Springer Verlag
Edition: 2011 ed.
Dimensions:
Width: 15.50cm
, Height: 3.80cm
, Length: 23.50cm
Weight: 1.116kg
ISBN: 9788847056275
ISBN 10: 8847056276
Pages: 721
Publication Date: 12 October 2014
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Language: English
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)
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. (Soren Christensen, Zentralblatt MATH, Vol. 1214, 2011)
Author Information
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).
