>Emanuel Derman
The Volatility Smile
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, visit our Web site at www.WileyFinance.com.
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 Volatility Smile
EMANUEL DERMAN
MICHAEL B. MILLER
with contributions by David Park
Cover image: Under the Wave off Kanagawa by Hokusai © Fine Art Premium / Corbis Images
Cover design: Wiley
Copyright © 2016 by Emanuel Derman and Michael B. Miller. 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 (978) 646-8600, 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 (201) 748-6008, or online at http://www.wiley.com/go/permissions.
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 for 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 (317) 572-4002.
Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com.
Library of Congress Cataloging-in-Publication Data:
Names: Derman, Emanuel, author. | Miller, Michael B. (Michael Bernard), 1973-author.
Title: The volatility smile / Emanuel Derman, Michael B. Miller.
Description: Hoboken, New Jersey: Wiley, 2016. | Series: The Wiley finance series | Includes index.
Identifiers: LCCN 2016012191 (print) | LCCN 2016019398 (ebook) | ISBN 9781118959169 (hardback) | ISBN 9781118959176 (pdf) | ISBN 9781118959183 (epub)
Subjects: LCSH: Finance–Mathematical models. | Securities–Valuation. | BISAC: BUSINESS & ECONOMICS / Finance.
Classification: LCC HG106 .D48 2016 (print) | LCC HG106 (ebook) | DDC 332.63/228301–dc23
LC record available at https://lccn.loc.gov/2016012191
My job, I believe, is to persuade others that my conclusions are sound. I will use an array of devices to do this: theory, stylized facts, time-series data, surveys, appeals to introspection, and so on.
Preface
Academic books and papers on finance have become regrettably formal over the past 30 years, filled with postulates, theorems, and lemmas. This axiomatic approach is suitable for presenting pure mathematics, but, in our view, is inappropriate for the field of finance. In finance, ideas should come first; mathematics is simply the language that we use to express ideas and elaborate their consequences.
We feel that the best way to learn and teach financial theory is to walk a middle line between the traditionally math-inclined academic and the stereotypically math-skeptical trader. This book tries to present a treatment of the volatility smile that combines the insight that comes from models with the practicality of the trading desk.
The first two chapters of this book provide a close look at the theory of modeling and the principles of valuation, themes that we return to again and again throughout the book. Chapters 3 through 13 explore the Black-Scholes-Merton option pricing model. At the heart of this model is a clash with the actual behavior of markets, the contradiction of the volatility smile. We show how, despite this flaw, there are productive ways to use not only the model itself, but the principles underlying it. Finally, in Chapters 14 through 24, we explore more advanced option models consistent with the smile. These models can be grouped into three families: local volatility, stochastic volatility, and jump-diffusion. While these newer models address many of the shortcomings of the Black-Scholes-Merton model, they are themselves imperfect. As markets evolve and traders gain experience, old models inevitably fail and need modification, or are replaced by newer models. Our hope is that the principles in this book will provide readers with the ability to develop and use their own models.
Acknowledgments
Emanuel Derman: Over the years I have benefited from enlightening conversations with, among many others, Iraj Kani, Mike Kamal, Joe Zou, the late Fischer Black, Peter Carr, Paul Wilmott, Nassim Taleb, Elie Ayache, Jim Gatheral, and Bruno Dupire. In particular, the influence of the work of Peter Carr and Paul Wilmott will be obvious in many chapters.
We thank Sebastien Bossu, Jesse Cole, and Tim Leung for helpful comments on the manuscript.
About the Authors
Emanuel Derman is a professor at Columbia University, where he directs the program in financial engineering. He was born in South Africa but has lived most of his professional life in Manhattan. He started out as a theoretical physicist,
