57,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley Finance Editions
- Sprache: Englisch
The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: * The principles of valuation * Static and dynamic replication * The Black-Scholes-Merton model * Hedging strategies * Transaction costs * The behavior of the volatility smile * Implied distributions * Local volatility models * Stochastic volatility models * Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 641
Veröffentlichungsjahr: 2016
Ähnliche
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.
—Fischer Black
List of Tables
Chapter 3
Table 3.1
Chapter 4
Table 4.1
Table 4.2
Table 4.3
Chapter 5
Table 5.1
Chapter 12
Table 12.1
Table 12.2
Table 12.3
Table 12.4
Chapter 13
Table 13.1
Chapter 17
Table 17.1
Chapter 18
Table 18.1
Answers to End-of-Chapter Problems
Table A4.1
Guide
Cover
Table of Contents
Preface
Pages
xi
xiii
xv
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
92
93
94
95
96
97
98
99
100
101
102
103
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
175
176
177
178
179
180
181
182
183
185
186
187
188
189
190
191
192
193
194
197
198
199
200
201
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
419
421
422
423
424
425
426
427
428
429
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
501
502
503
504
505
506
507
508
509
510
511
512
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, doing research on unified theories of elementary particle interactions. At AT&T Bell Laboratories in the 1980s he developed programming languages for business modeling. From 1985 to 2002 he worked on Wall Street, where he codeveloped the Black-Derman-Toy interest rate model and the local volatility model. His previous books, My Life as a Quant and Models.Behaving.Badly, were both among BusinessWeek's top 10 annual books.
Michael B. Miller is the founder and CEO of Northstar Risk Corp. Before starting Northstar, he was the chief risk officer for Tremblant Capital and before that the head of quantitative risk management at Fortress Investment Group. He is the author of Mathematics and Statistics for Financial Risk Management, now in its second edition, and an adjunct professor at Rutgers Business School. Before starting his career in finance, he studied economics at the American University of Paris and the University of Oxford.
Joo-Hyung (David) Park has extensive experience in valuation of financial instruments and derivatives. He provides valuation advisory services to corporate and private equity clients for their holdings in nonstandard derivative products. These products include equity options granted to executives, embedded derivatives in convertible bonds, and many other customized fixed income and equity derivatives. Prior to this, he studied financial engineering at Columbia University, and physics at the University of Toronto.
Chapter 2The Principle of Replication
The law of one price: Similar things must have similar prices.
Replication: the only reliable way to value a security.
A simple up-down model for the risk of stocks, in which expected return
μ
and volatility
σ
are all that matter.
The law of one price leads to CAPM for stocks.
Replicating derivatives via the law of one price.
Replication
Replication is the strategy of creating a portfolio of securities that closely mimics the behavior of another security. In this section we will see how replication can be used to value a security of interest. We define different styles of replication, and discuss the power and limits of this method of valuation.
The One Law of Quantitative Finance
Hillel, a famous Jewish sage, when asked to recite the essence of God's laws while standing on one leg, replied:
Do not do unto others as you would not have them do unto you. All the rest is commentary. Go and learn.
Andrew Lo, a professor at MIT, has quipped that while physics has three laws that explain 99% of the phenomena, finance has 99 laws that explain only 3%. It's a funny joke at finance's expense, but finance actually has one more or less reliable law that forms the basis of almost all of quantitative finance.
Though it is often stated in different ways, you can summarize the essence of quantitative finance somewhat like Hillel, on one leg:
If you want to know the value of a security, use the price of another security or set of securities that's as similar to it as possible. All the rest is modeling. Go and build.
This is the law of analogy: If you want to value something, do it by comparing it to something else whose price you already know.
Financial economists like a different statement of this principle, which they call the law of one price:
If two securities have identical payoffs under all possible future scenarios, then the two securities should have identical current prices.
If two securities (or portfolios of securities) with identical payoffs were to have different prices, you could buy the cheaper one and short the more expensive one, immediately pocket the difference, and experience no positive or negative cash flows in the future, since the payoffs of the long and short positions would always exactly cancel.
In practice, we will rarely be able to construct a replicating portfolio that is exactly the same in all scenarios. We may have to settle for a replicating portfolio that is approximately the same in most scenarios.
What both of the aforementioned formulations hint at is the impossibility of arbitrage, the ability to trade in such a way that will guarantee a profit without any risk. Another version of the law of one price is therefore the principle of no riskless arbitrage, which can be stated as follows:
It should be impossible to obtain for zero cost a security that has nonnegative payoffs in all future scenarios, with at least one scenario having a positive payoff.
