Equity Derivatives E-Book

Marcus Overhaus

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Editions
• Sprache: Englisch

Seitenzahl: 301

Veröffentlichungsjahr: 2011

Beschreibung

Written by the quantitative research team of Deutsche Bank, the world leader in innovative equity derivative transactions, this book acquaints readers with leading-edge thinking in modeling and hedging these transactions. Equity Derivatives offers a balanced, integrated presentation of theory and practice in equity derivative markets. It provides a theoretical treatment of each new modeling and hedging concept first, and then demonstrates their practical application. The book covers: the newest and fastest-growing class of derivative instruments, fund derivatives; cutting-edge developments in equity derivative modeling; new developments in correlation modeling and understanding volatility skews; and new Web-based implementation/delivery methods. Marcus Overhaus, PhD, Andrew Ferraris, DPhil, Thomas Knudsen, PhD, Frank Mao, PhD, Ross Milward, Laurent Nguyen-Ngoc, PhD, and Gero Schindlmayr, PhD, are members of the Quantitative Research team of Deutsche Bank's Global Equity Division, which is based in London and headed by Dr. Overhaus.

Leseprobe

Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding.

The Wiley Finance series contains books written specifically for finance and investment professionals as well as sophisticated individual investors and their financial advisors. Book topics range from portfolio management to e-commerce, risk management, financial engineering, valuation, and financial instrument analysis, as well as much more. For a list of available titles, please visit our web site at www.WileyFinance.com.

Copyright © 2002 by Marcus Overhaus. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax [phone], or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax [phone], e-mail: [email protected].

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services, or technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax [phone].

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.

Library of Congress Cataloging-in-Publication Data:

Overhaus, Marcus.

Equity derivatives: theory and applications / Marcus Overhaus.

p. cm.

Includes index.

ISBN 0-471-43646-1 (cloth : alk. paper)

1. Derivative securities. I. Title.

HG6024.A3 O94 2001

332.63’2-dc21 2001026547

About the Authors

Marcus Overhaus is Managing Director and Global Head of Quantitative Research at Deutsche Bank AG. He holds a Ph.D. in pure mathematics.

Andrew Ferraris is a Director in Global Quantitative Research at Deutsche Bank AG. His work focuses on the software design of the model library and its integration into client applications. He holds a D.Phil. in experimental particle physics.

Thomas Knudsen is a Vice President in Global Quantitative Research at Deutsche Bank AG. His work focuses on modeling volatility. He holds a Ph.D. in pure mathematics.

Ross Milward is a Vice President in Global Quantitative Research at Deutsche Bank AG. His work focuses on the architecture of analytics services and web technologies. He holds a B.Sc. (Hons.) in computer science.

Laurent Nguyen-Ngoc works in Global Quantitative Research at Deutsche Bank AG. His work focuses on Lévy processes applied to volatility modeling. He is completing a Ph.D. in probability theory.

Gero Schindlmayr is an Associate in Global Quantitative Research at Deutsche Bank AG. His work focuses on finite difference techniques. He holds a Ph.D. in pure mathematics.

Preface

Equity derivatives and equity-linked structures—a story of success that still continues. That is why, after publishing two books already, we decided to publish a third book on this topic. We hope that the reader of this book will participate and enjoy this very dynamic and profitable business and its associated complexity as much as we have done, still do, and will continue to do.

Our approach is, as in our first two books, to provide the reader with a self-contained unit. Chapter 1 starts with a mathematical foundation for all the remaining chapters. Chapter 2 is dedicated to pricing and hedging in incomplete markets. In Chapter 3 we give a thorough introduction to Lévy processes and their application to finance, and we show how to push the Heston stochastic volatility model toward a much more general framework: the Heston Jump Diffusion model.

How to set up a general multifactor finite difference framework to incorporate, for example, stochastic volatility, is presented in Chapter 4. Chapter 5 gives a detailed review of current convertible bond models, and expounds a detailed discussion of convertible bond asset swaps (CBAS) and their advantages compared to convertible bonds.

Chapters 6, 7, and 8 deal with recent developments and new technologies in the delivery of pricing and hedging analytics over the Internet and intranet. Beginning by outlining XML, the emerging standard for representing and transmitting data of all kinds, we then consider the technologies available for distributed computing, focusing on SOAP and web services. Finally, we illustrate the application of these technologies and of scripting technologies to providing analytics to client applications, including web browsers.

Chapter 9 describes a portfolio and hedging simulation engine and its application to discrete hedging, to hedging in the Heston model, and to CPPIs. We have tried to be as extensive as we could regarding the list of references: Our only regret is that we are unlikely to have caught everything that might have been useful to our readers.

We would like to offer our special thanks to Marc Yor for careful reading of the manuscript and valuable comments.

The Authors

London, November 2001

CONTENTS

Chapter 1: Mathematical Introduction

1.1 Probability Basis

1.2 Processes

1.3 Stochastic Calculus

1.4 Financial Interpretations

1.5 Two Canonical Examples

Chapter 2: Incomplete Markets

2.1 Martingale Measures

2.2 Self-Financing Strategies, Completeness, and No Arbitrage

2.3 Examples

2.4 Martingale Measures, Completeness, and No Arbitrage

2.5 Completing the Market

2.6 Pricing in Incomplete Markets

2.7 Variance-Optimal Pricing and Hedging

2.8 Super Hedging and Quantile Hedging

Chapter 3: Financial Modeling with Lévy Processes

3.1 A Primer on Lévy Processes

3.2 Modeling with Lévy Processes

3.3 Products and Models

3.4 Model Calibration and Smile Replication

3.5 Numerical Methods for Lévy Processes

3.6 A Model Involving Lévy Processes

Chapter 4: Finite-Difference Methods for Multifactor Models

4.1 Pricing Models and PDEs

4.2 The Pricing PDE and Its Discretization

4.3 Explicit and Implicit Schemes

4.4 The ADI Scheme

4.5 Convergence and Performance

4.6 Dividend Treatment in Stochastic Volatility Models

Chapter 5: Convertible Bonds and Asset Swaps

5.1 Convertible Bonds

5.2 Convertible Bond Asset Swaps

Chapter 6: Data Representation

6.1 XML

6.2 XML Schema

6.3 XML Transformation

6.4 Representing Equity Derivative Market Data

Chapter 7: Application Connectivity

7.1 Components

7.2 Distributed Components

7.3 SOAP

7.4 Web Services

Chapter 8: Web-Based Quantitative Services

8.1 Web Pricing Servers

8.2 Model Integration into Risk Management and Booking Systems

8.3 Web Applications and Dynamic Web Pages

Chapter 9: Portfolio and Hedging Simulation

9.1 Introduction

9.2 Algorithm and Software Design

9.3 Example: Discrete Hedging and Volatility Misspecification

9.4 Example: Hedging a Heston Market

9.5 Example: Constant Proportion Portfolio Insurance

9.6 Server Integration

References

Index

CHAPTER 1

Mathematical Introduction

The use of probability theory and stochastic calculus is now an established standard in the field of financial derivatives. During the last 30 years, a large amount of material has been published, in the form of books or papers, on both the theory of stochastic processes and their applications to finance problems. The goal of this chapter is to introduce notions on probability theory and stochastic calculus that are used in the applications presented afterwards. The notations used here will remain identical throughout the book.

We hope that the reader who is not familiar with the theory of stochastic processes will find here an intuitive presentation, although rigorous enough for our purposes, and a set of useful references about the underlying mathematical theory. The reader acquainted with stochastic calculus will find here an introduction of objects and notations that are used constantly, although maybe not very explicitly.

This chapter does not aim at giving a thorough treatment of the theory of stochastic processes, nor does it give a detailed view of mathematical finance theory in general. It recalls, rather, the main general facts that will be used in the examples developed in the next chapters.

1.1 PROBABILITY BASIS

Financial models used for the evaluation of derivatives are mainly concerned with the uncertainty of the future evolution of the stock prices. The theory of probability and stochastic processes provides a framework with a form of uncertainty, called randomness. A probability spaceΩ is assumed to be given once and for all, interpreted as consisting of all the possible paths of the prices of securities we are interested in. We will suppose that this probability space is rich enough to carry all the random objects we wish to construct and use. This assumption is not restrictive for our purposes, because we could always enlarge the space Ω, for example, by considering a product space. Note that Ω can be chosen to be a “canonical space,” such as the space of continuous functions, or the space of cadlag (French acronym for “continuous from the right, with left limits”) functions.

We endow the set Ω with a σ-field which is also assumed to be fixed throughout this book, unless otherwise specified. represents all the events that are or will eventually be observable.

Let be a probability measure on the measurable space (Ω, ). The (Lebesgue) integral with respect to of a random variable X (that is, a measurable function from (Ω, ) to (N, N), where N is the Borel σ-field on N) is denoted by [X] instead of ∫ΩX d and is called the expectation of X. If we need to emphasize that the expectation operator is relative to , we denote it by . We assume that the reader is familiar with general notions of probability theory such as independence, correlation, conditional expectation, and so forth. For more details and references, we refer to [9], [45], or [49].