Derivative Securities and Difference Methods

ISBN-13: 9781441919250 / Angielski / Miękka / 2011 / 513 str.

You-Lan Zhu; Xiaonan Wu; I-Liang Chern

Opis

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."

Recenzje

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)

Spis treści

Part I - Partial Differential Equations in Finance * Introduction * Basic Options * Exotic Options * Interest Rate Derivative Securities * Part II - Numerical Methods for Derivative Securities * Basic Numerical Methods * Initial-Boundary Value and LC Problems * Free Boundary Problems * Interest Rate Modeling * References * Index

Blurb

 

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.