Derivative Securities and Difference Methods

The book "Derivative Securities and Difference Methods" offers a comprehensive analysis of finite difference methods for solving partial differential equations (PDEs) that are relevant for pricing a variety of financial derivatives. It is divided into two main parts. The first part covers the fundamentals of derivative securities and explains how to formulate appropriate PDE boundary value problems for different derivatives, including vanilla and exotic options as well as interest rate derivatives. Analytical solutions for many options problems are derived in detail. The second part focuses on the application of finite difference techniques to the financial models discussed in part one. It addresses fundamental concepts of finite difference methods as well as specific issues such as linear complementarity and free boundary problems. This textbook is aimed at students of mathematical finance and also serves as a valuable reference for researchers in the field of numerical methods for financial derivatives. The updated edition includes numerous new problems and examples that illustrate the application of numerical methods.