Ebook: Derivative Securities and Difference Methods

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. With this objective, the book is divided into two main parts.

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. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems. In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products. This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods in financial derivatives. For this new edition, the book has been updated throughout with many new problems added. 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 two-dimensional problems are added.

Review 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

This book is mainly devoted to finite difference numerical methods for solving partial differential equation (PDE) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.

In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE initial/initial-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. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems. In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products.

This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods of financial derivatives. For this new edition, the book has been updated throughout with many new problems added. 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 two-dimensional problems are added.

Review 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, 2005

This book is mainly devoted to finite difference numerical methods for solving partial differential equation (PDE) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.

In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE initial/initial-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. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems. In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products.

This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods of financial derivatives. For this new edition, the book has been updated throughout with many new problems added. 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 two-dimensional problems are added.

Review 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, 2005

Content:
Front Matter....Pages i-xxii
Front Matter....Pages 1-1
Introduction....Pages 3-15
European Style Derivatives....Pages 17-103
American Style Derivatives....Pages 105-157
Exotic Options....Pages 159-275
Interest Rate Derivative Securities....Pages 277-345
Front Matter....Pages 347-347
Basic Numerical Methods....Pages 349-389
Finite-Difference Methods....Pages 391-444
Initial-Boundary Value and LC Problems....Pages 445-534
Free-Boundary Problems....Pages 535-604
Interest Rate Modeling....Pages 605-636
Back Matter....Pages 637-647

This book is mainly devoted to finite difference numerical methods for solving partial differential equation (PDE) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.

In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE initial/initial-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. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems. In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products.

This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods of financial derivatives. For this new edition, the book has been updated throughout with many new problems added. 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 two-dimensional problems are added.

Review 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, 2005

Content:
Front Matter....Pages i-xxii
Front Matter....Pages 1-1
Introduction....Pages 3-15
European Style Derivatives....Pages 17-103
American Style Derivatives....Pages 105-157
Exotic Options....Pages 159-275
Interest Rate Derivative Securities....Pages 277-345
Front Matter....Pages 347-347
Basic Numerical Methods....Pages 349-389
Finite-Difference Methods....Pages 391-444
Initial-Boundary Value and LC Problems....Pages 445-534
Free-Boundary Problems....Pages 535-604
Interest Rate Modeling....Pages 605-636
Back Matter....Pages 637-647
....