This book is mainly devoted to finite difference numerical methods for
solving partial differential equations (PDEs) models of pricing a wide
variety of financial derivative securities. With this objective, the
book is divided into two main parts.
In the first part, after an introduction concerning the basics on
derivative securities, the authors explain how to establish the adequate
PDE boundary value problems for different sets of derivative products
(vanilla and exotic options, and interest rate derivatives). For many
option problems, the analytic solutions are also derived with details.
The second part is devoted to explaining and analyzing the application
of finite differences techniques to the financial models stated in the
first part of the book. For this, the authors recall some basics on
finite difference methods, initial boundary value problems, and (having
in view financial products with early exercise feature) linear
complementarity and free boundary problems. In each chapter, the
techniques related to these mathematical and numerical subjects are
applied to a wide variety of financial products. This is a textbook for
graduate students following a mathematical finance program as well as a
valuable reference for those researchers working in numerical methods in
financial derivatives. For this new edition, the book has been updated
throughout with many new problems added. More details about numerical
methods for some options, for example, Asian options with discrete
sampling, are provided and the proof of solution-uniqueness of
derivative security problems and the complete stability analysis of
numerical methods for two-dimensional problems are added.
Review of first edition:
"...the book is highly well designed and structured as a textbook for
graduate students following a mathematical finance program, which
includes Black-Scholes dynamic hedging methodology to price financial
derivatives. Also, it is a very valuable reference for those researchers
working in numerical methods in financial derivatives, either with a
more financial or mathematical background." -- MATHEMATICAL REVIEWS
