Overview
Presented in two parts, this book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a variety of financial derivative securities. 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.\xa0The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part. The authors recall some basics on finite difference methods, initial boundary value problems, and linear complementarity and free boundary problems. Techniques related to mathematical and numerical subjects are applied to financial products. This is a textbook for graduate students and a valuable reference for researchers working in numerical methods in financial derivatives. This edition has been updated throughout. 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 2-dimensional problems are added.\xa0\xa0Review 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
