My Life as a Quant

Contents

Prologue

Chapter 1: Elective Affinities

Chapter 2: Dog Years

Chapter 3: A Sort of Life

Chapter 4: A Sentimental Education

Chapter 5: The Mandarins

Chapter 6: Knowledge of the Higher Worlds

Chapter 7: In the Penal Colony

Chapter 8: Stop-Time

Chapter 9: Transformer

Chapter 10: Easy Travel to Other Planets

Chapter 11: Force of Circumstance

Chapter 12: A Severed Head

Chapter 13: Civilization and Its Discontents

Chapter 14: Laughter in The Dark

Chapter 15: The Snows of Yesteryear

Chapter 16: The Great Pretender

Acknowledgments

About the Author

Index

More Praise for
My Life as a Quant

“An honest account of the experience of going from an environment of Nobel Prize winners and pure thought to one of money, money, money. Derman gives us unique insight into the motivations of academia, the pressure to cast off worldly success in favor of matters more cerebral, then the mixed feelings during his descent into a world where the bottom line is P&L, and finally his success at bringing his own style of science into investment banking.”

—Paul Wilmottt, mathematician, author, and fund manager

“A fascinating personal account of one man's journey through several of the leading institutions of our time. Written by perhaps the leading practitioner of his generation, this insightful narrative explores the disparate cultures of physics, finance, and their powerful fusion known as phynance. This book is a must-read for aspiring quants, financial historians, and armchair sociologists interested in the machinations of both academia and industry.”

—Peter Carr, Head of Quantitative Research, Bloomberg, and Director, Masters in Math Finance, NYU

Copyright © 2004 by Emanuel Derman. 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.

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 317-572-4002.

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

For more information about Wiley products, visit our Web site at
www.wiley.com
.

Library of Congress Cataloging-in-Publication Data

Derman, Emanuel.

My life as a quant : reflections on physics and finance / Emanuel Derman.

p. cm.

Includes biographical references and index.

ISBN 978-0-471-39420-4 (cloth)

ISBN 978-0-470-19273-3 (paper)

1. Derman, Emanuel 2. Investment advisors—Biography. 3. Physicists—Biography. 4. Options (Finance) 5. Quantum theory. 6. Mathematical physics. I. Title.

HG4621.D47 2004

332.6'092—dc22

2004007664

To the Memory of My Parents

Prologue

The Two Cultures

Physics and finance

What quants do

The Black-Scholes model

Quants and traders

Pure thought and beautiful mathematics can divine the laws of physics

Can they do the same for finance?

If mathematics is the Queen of Sciences, as the great mathematician Karl Friedrich Gauss christened it in the nineteenth century, then physics is king. From the mid-seventeenth century to the end of the nineteenth, Newton's Law of Gravitation, his three Laws of Motion, and his differential calculus described with apparent perfection the mechanical motion of objects in our world and the solar system.

In 1864, two hundred years after Newton, the Scottish physicist James Clerk Maxwell formulated the compact and elegant differential equations that described with similarly astounding precision the propagation of light, X-rays, and radio waves. Maxwell's equations showed that electricity and magnetism, formerly separate phenomena, were part of the same unified electromagnetic field.

We cannot simply look at the world around us and deduce Newton's Laws or Maxwell's equations. Data on its own does not speak. These equations were triumphs of the mind, abstracted from the world in some miraculous confluence of hard thinking and deep intuition. Their success confirmed that pure thought and beautiful mathematics have the power to discover the most profound laws of the universe.

At the start of the twentieth century, the pace accelerated. Einstein, pondering the conflicts between the Newtonian and Maxwellian views of the world, proposed his Theory of Special Relativity that amended Newton's mechanics and made them consistent with Maxwell's equations. Fifteen years later Einstein trumped Newton again with his proposal of the General Theory; it corrected the Law of Gravitation and described gravity as a large-scale wave in space and time. At almost the same time, Bohr, Schrödinger, and Heisenberg, with help from the ever-prodigious Einstein, developed the quantum mechanical theory of the small-scale behavior of molecules, atoms, and subatomic particles.

It was Einstein who perfected this mental approach to discovering the laws of the universe. His method wasn't based on observation or empiricism; he tried to perceive and then enunciate the very principles that constrained the way things should work. In a 1918 speech on the principles of research given in honor of Max Planck, the discoverer of the quantum, Einstein captured the magus-like appeal of trying to see through a glass, darkly, when he said: “There is no logical path to these laws; only intuition, resting on a sympathetic understanding of experience, can reach them.”

What is the purpose behind the search for scientific laws, in any field? Clearly, it's divination—foretelling the future, and controlling it. Most of the modern technologies we enjoy, rely on, detest, or fear—cell phones, electric power grids, CAT scans, and nuclear weapons, for example—have been developed by using the basic principles of quantum mechanics, electromagnetic theory, and relativity, all of which were discovered by cerebration. The classic tools of twentieth-century divination have indeed been those of physics. More recently, physicists have begun to employ the same tools in finance.

For the past twenty years, throughout Wall Street and the City of London, in most major and many minor financial institutions, small groups of ex-physicists and applied mathematicians have tried to apply their skills to securities markets. Formerly called “rocket scientists” by those who mistakenly thought that rocketry was the most advanced branch of science, they are now commonly called “quants.”

Quants and their cohorts practice “financial engineering”—an awkward neologism coined to describe the jumble of activities that would better be termed
quantitative finance
. The subject is an interdisciplinary mix of physics-inspired models, mathematical techniques, and computer science, all aimed at the valuation of financial securities. The best quantitative finance brings real insight into the relation between value and uncertainty, and it approaches the quality of real science; the worst is a pseudoscientific hodgepodge of complex mathematics used with obscure justification.

Until recently, financial engineering wasn't really a subject at all—when I entered the field in 1985, it didn't have a name and was something one learned on the job at an investment bank. Now you can get a master's degree in the subject at scores of institutions—the Courant Institute at New York University, the University of Michigan at Ann Arbor, and the University of Oregon in Eugene, to name a few. Since July 2003 I have been a professor of the subject at Columbia University. Engineering schools, statistics and mathematics departments, and business schools organize these one- to two-year programs; they promise to transform students, in exchange for about $30,000 per year, into employable financial engineers. So popular are these degrees that some universities run several similar programs in distinct departments.

Nowadays, managers on Wall Street receive daily calls and emailed résumés from PhDs seeking jobs in finance. Physics journals publish increasing numbers of papers on financial economics. And increasingly, physicists and mathematicians working on the quantitative side of banking have been joined by PhDs and faculty members from finance departments and business schools. Two of the best graduate finance departments in the country, the Sloan School at MIT and the Haas School of the University of California at Berkeley, have each lost several of their best young finance faculty to the banking and trading worlds.

Part of the reason for the influx of physicists to other fields was the 1970s collapse of their traditional job market: academia. Thirty years earlier during World War II, the invention of radar and the construction of the atomic bomb confirmed the usefulness of physics to postwar governments. Shocked by the successful voyage of Sputnik, the Departments of Defense and Energy began to fund pure research more copiously, and physicists seeking grants to do such research weren't above playing up the spin-off benefits of their work. Physics departments in the 1960s grew and academic posts multiplied. Inspired by the subject and supported by scholarships, a wave of ardent graduate students entered the field.

The good times didn't last. By the end of the Vietnam War a deteriorating economy and a public revulsion with science in the service of war put a large dent in research funds. During the 1970s and 1980s, many theoretical physicists who had once hoped to devote their lives to fundamental research were forced to become migratory laborers if they wanted to remain in academia, taking temporary short-term positions in universities and national laboratories wherever they became available. Many of us eventually gave up the struggle to find even a low-paying semipermanent academic job and turned to other areas. We sought physics-related jobs in a variety of fields—in energy research or telecommunications, for example. Former colleagues of mine began to work on alternate power sources at the Solar Energy Research Institute in Golden, Colorado, or on the mathematics of oil retrieval at Schlumberger in Ridgefield, Connecticut. Others helped develop advanced switching systems at AT&T's Bell Laboratories in New Jersey.