Derivative Securities and Difference Methods

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 app roach 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.

Inhaltsverzeichnis:

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.

Rezension:

From the reviews:

"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... 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

"This book is devoted to pricing financial derivatives with a partial differential equation approach. It has two parts, each with four chapters. ... The book covers a variety of topics in finance, such as forward and futures contracts, the Black-Scholes model, European and American type options, free boundary problems, barrier options, lookback options, multi-asset options, interest rate models, interest rate derivatives, swaps, swaptions, caps, floors, and collars. The treatment is mathematically rigorous. There are exercises at the end of each chapter." (Elias Shiu, Zentralblatt MATH, Vol. 1061 (12), 2005)