Derivative Securities and Difference Methods

This book provides an overview of the theory of pricing financial derivatives and presents finite difference methods for numerically approximating derivative prices.

Currently there are no other books covering this topic There is a need for a book of this type in the rapidly developing area of Computational Finance Includes supplementary material: sn.pub/extras

Texte du rabat

This book is devoted to determining the prices of financial derivatives using a partial differential equation approach. In the first part the authors describe the formulation of the problems (including related free-boundary problems) and derive the closed form solutions if they have been found. The second part discusses how to obtain their numerical solutions efficiently for both European-style and American-style derivatives and for both stock options and interest rate derivatives. The numerical methods discussed are finite-difference methods. The book also discusses how to determine the coefficients in the partial differential equations.

The aim of the book is to provide readers who have some code writing experience for engineering computations with the skills to develop efficient derivative-pricing codes. The book includes exercises throughout and will appeal to students and researchers in quantitative finance as well as practitioners in the financial industry and code developers.

Résumé
In the past three decades, great progress has been made in the theory and prac­ tice of financial derivative securities. Now huge volumes of financial derivative securities are traded on the market every day. This causes a big demand for experts who know how to price financial derivative securities. This book is designed as a textbook for graduate students in a mathematical finance pro­ gram and as a reference book for the people who already work in this field. We hope that a person who has studied this book and who knows how to write codes for engineering computation can handle the business of providing efficient derivative-pricing codes. In order for this book to be used by various people, the prerequisites to study the majority of this book are multivariable calculus, linear algebra, and basic probability and statistics. In this book, the determination of the prices of financial derivative secu­ rities is reduced to solving partial differential equation problems, i. e. , a PDE approach is adopted in order to find the price of a derivative security. This book is divided into two parts. In the first part, we discuss how to establish the corresponding partial differential equations and find the final and nec­ essary boundary conditions for a specific derivative product. If possible, we derive its explicit solution and describe some properties of the solution. In many cases, no explicit solution has been found so far.

Contenu
1 Introduction.- 2 Basic Options.- 3 Exotic Options.- 4 Interest Rate Derivative Securities.- 5 Basic Numerical Methods.- 6 Initial-Boundary Value and LC Problems.- 7 Free-Boundary Problems.- 8 Interest Rate Modeling.- References.