50,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley Finance Editions
- Sprache: Englisch
A clear, practical guide to working effectively with derivative securities products Derivatives Essentials is an accessible, yet detailed guide to derivative securities. With an emphasis on mechanisms over formulas, this book promotes a greater understanding of the topic in a straightforward manner, using plain-English explanations. Mathematics are included, but the focus is on comprehension and the issues that matter most to practitioners--including the rights and obligations, terms and conventions, opportunities and exposures, trading, motivation, sensitivities, pricing, and valuation of each product. Coverage includes forwards, futures, options, swaps, and related products and trading strategies, with practical examples that demonstrate each concept in action. The companion website provides Excel files that illustrate pricing, valuation, sensitivities, and strategies discussed in the book, and practice and assessment questions for each chapter allow you to reinforce your learning and gauge the depth of your understanding. Derivative securities are a complex topic with many "moving parts," but practitioners must possess a full working knowledge of these products to use them effectively. This book promotes a truly internalized understanding rather than rote memorization or strict quantitation, with clear explanations and true-to-life examples. * Understand the concepts behind derivative securities * Delve into the nature, pricing, and offset of sensitivities * Learn how different products are priced and valued * Examine trading strategies and practical examples for each product Pricing and valuation is important, but understanding the fundamental nature of each product is critical--it gives you the power to wield them more effectively, and exploit their natural behaviors to achieve both short- and long-term market goals. Derivatives Essentials provides the clarity and practical perspective you need to master the effective use of derivative securities products.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 402
Veröffentlichungsjahr: 2016
Ähnliche
Table of Contents
Preface
Acknowledgments
About the Author
Part One: Introduction to Forwards, Futures, and Options
Chapter 1: Forwards and Futures
Introduction
1.1 Forward contract characteristics
1.2 Long forward payoff
1.3 Long forward P&L
1.4 Short forward payoff
1.5 Short forward P&L
1.6 Long forward P&L diagram
1.7 Short forward P&L diagram
1.8 Forwards are zero-sum games
1.9 Counterparty credit risk
1.10 Futures contracts
Key Points
Chapter 2: Call Options
Introduction
2.1 Call option characteristics
2.2 Long call payoff
2.3 Long call P&L
2.4 Short call payoff
2.5 Short call P&L
2.6 Long call P&L diagram
2.7 Short call P&L diagram
2.8 Call options are zero-sum games
2.9 Call option moneyness
2.10 Exercising a call option early
2.11 Comparison of call options and forwards/futures
Key Points
Chapter 3: Put Options
Introduction
3.1 Put option characteristics
3.2 Long put payoff
3.3 Long put P&L
3.4 Short put payoff
3.5 Short put P&L
3.6 Long put P&L diagram
3.7 Short put P&L diagram
3.8 Put options are zero-sum games
3.9 Put option moneyness
3.10 Exercising a put option early
3.11 Comparison of put options, call options, and forwards
Key Points
Part Two: Pricing and Valuation
Chapter 4: Useful Quantitative Concepts
Introduction
4.1 Compounding conventions
4.2 Calculating future value and present value
4.3 Identifying continuously compounded interest rates
4.4 Volatility and historical standard deviation
4.5 Interpretation of standard deviation
4.6 Annualized standard deviation
4.7 The standard normal cumulative distribution function
4.8 The z-score
Key Points
Chapter 5: Introduction to Pricing and Valuation
Introduction
5.1 The concepts of price and value of a forward contract
5.2 The concepts of price and value of an option
5.3 Comparison of price and value concepts for forwards and options
5.4 Forward value
5.5 Forward price
5.6 Option value: The Black-Scholes model
5.7 Calculating the Black-Scholes model
5.8 Black-Scholes model assumptions
5.9 Implied volatility
Key Points
Chapter 6: Understanding Pricing and Valuation
Introduction
6.1 Review of payoff, price, and value equations
6.2 Value as the present value of expected payoff
6.3 Risk-neutral valuation
6.4 Probability and expected value concepts
6.5 Understanding the Black-Scholes equation for call value
6.6 Understanding the Black-Scholes equation for put value
6.7 Understanding the equation for forward value
6.8 Understanding the equation for forward price
Key Points
Chapter 7: The Binomial Option Pricing Model
Introduction
7.1 Modeling discrete points in time
7.2 Introduction to the one-period binomial option pricing model
7.3 Option valuation, one-period binomial option pricing model
7.4 Two-period binomial option pricing model, European-style option
7.5 Two-period binomial model, American-style option
7.6 Multi-period binomial option pricing models
Key Points
Part Three: The Greeks
Chapter 8: Introduction to the Greeks
Introduction
8.1 Definitions of the Greeks
8.2 Characteristics of the Greeks
8.3 Equations for the Greeks
8.4 Calculating the Greeks
8.5 Interpreting the Greeks
8.6 The accuracy of the Greeks
Key Points
Chapter 9: Understanding Delta and Gamma
Introduction
9.1 Describing sensitivity using Delta and Gamma
9.2 Understanding Delta
9.3 Delta across the underlying asset price
9.4 Understanding Gamma
9.5 Gamma across the underlying asset price
Key Points
Chapter 10: Understanding Vega, Rho, and Theta
Introduction
10.1 Describing sensitivity using Vega, Rho, and Theta
10.2 Understanding Vega
10.3 Understanding Rho
10.4 Understanding Theta
Key Points
Part Four: Trading Strategies
Chapter 11: Price and Volatility Trading Strategies
Introduction
11.1 Price and volatility views
11.2 Relating price and volatility views to Delta and Vega
11.3 Using forwards, calls, and puts to monetize views
11.4 Introduction to straddles
11.5 Delta and Vega characteristics of long and short straddles
11.6 The ATM DNS strike price
11.7 Straddle: numerical example
11.8 P&L diagrams for long and short straddles
11.9 Breakeven points for long and short straddles
11.10 Introduction to strangles
11.11 P&L diagrams for long and short strangles
11.12 Breakeven points for long and short strangles
11.13 Summary of simple price and volatility trading strategies
Key Points
Chapter 12: Synthetic, Protective, and Yield-Enhancing Trading Strategies
Introduction
12.1 Introduction to put-call parity and synthetic positions
12.2 P&L diagrams of synthetic positions
12.3 Synthetic positions premiums and ATMF
12.4 The Greeks of synthetic positions
12.5 Option arbitrage
12.6 Protective puts
12.7 Covered calls
12.8 Collars
Key Points
Chapter 13: Spread Trading Strategies
Introduction
13.1 Bull and bear spreads using calls
13.2 Bull and bear spreads using puts
13.3 Risk reversals
13.4 Butterfly spreads
13.5 Condor spreads
Key Points
Part Five: Swaps
Chapter 14: Interest Rate Swaps
Introduction
14.1 Interest rate swap characteristics
14.2 Interest rate swap cash flows
14.3 Calculating interest rate swap cash flows
14.4 How interest rate swaps can transform cash flows
Key Points
Chapter 15: Credit Default Swaps, Cross-Currency Swaps, and Other Swaps
Introduction
15.1 Credit default swap characteristics
15.2 Key determinants of the credit default swap spread
15.3 Cross-currency swap characteristics
15.4 Transforming cash flows using a cross-currency swap
15.5 Other swap varieties
Key Points
Appendix: Solutions to Knowledge Check Questions
A.1 Chapter 1: Forwards and Futures
A.2 Chapter 2: Call Options
A.3 Chapter 3: Put Options
A.4 Chapter 4: Useful Quantitative Concepts
A.5 Chapter 5: Introduction to Pricing and Valuation
A.6 Chapter 6: Understanding Pricing and Valuation
A.7 Chapter 7: The Binomial Option Pricing Model
A.8 Chapter 8: Introduction to the Greeks
A.9 Chapter 9: Understanding Delta and Gamma
A.10 Chapter 10: Understanding Vega, Rho, and Theta
A.11 Chapter 11: Price and Volatility Trading Strategies
A.12 Chapter 12: Synthetic, Protective, and Yield-Enhancing Trading Strategies
A.13 Chapter 13: Spread Trading Strategies
A.14 Chapter 14: Interest Rate Swaps
A.15 Chapter 15: Credit Default Swaps, Cross-Currency Swaps, and Other Swaps
Index
End User License Agreement
Pages
ii
iii
iv
v
xiii
xiv
xv
xvii
xix
1
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
56
57
58
59
60
61
62
63
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
91
92
93
94
95
96
97
98
99
100
101
102
103
104
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
130
131
132
133
134
135
136
137
138
139
140
141
143
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
174
175
176
177
178
179
180
181
182
183
184
185
186
187
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
243
244
245
246
247
248
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
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
Guide
Table of Contents
Begin Reading
List of Illustrations
Chapter 1: Forwards and Futures
Figure 1.1 Forward contract cash flows
Figure 1.2 Forward contract cash flows example
Figure 1.3 Forward contract cash flows example
Figure 1.4 Long forward payoff example
Figure 1.5 Long forward P&L example
Figure 1.6 Short forward payoff example
Figure 1.7 Short forward P&L example
Figure 1.8 Long forward P&L diagram
Figure 1.9 Long forward P&L diagram
Figure 1.10 Short forward P&L diagram
Figure 1.11 Short forward P&L diagram
Figure 1.12 Forward contract as a zero-sum game
Chapter 2: Call Options
Figure 2.1 European-style call option cash flows
Figure 2.2 European-style call option cash flows example
Figure 2.3 Long call P&L diagram
Figure 2.4 Long call P&L diagram example
Figure 2.5 Short call P&L diagram
Figure 2.6 Short call P&L diagram
Figure 2.7 Call option as a zero-sum game
Chapter 3: Put Options
Figure 3.1 European-style put option cash flows
Figure 3.2 European-style put option cash flows example
Figure 3.3 Long put P&L diagram
Figure 3.4 Long put P&L diagram example
Figure 3.5 Short put P&L diagram
Figure 3.6 Short put P&L diagram example
Figure 3.7 Put option as a zero-sum game
Chapter 4: Useful Quantitative Concepts
Figure 4.1 Growth of an investment that receives 5% over one year
Figure 4.2 Growth of an investment that receives 2.5% for two six-month periods
Figure 4.3 Probability of return above or below the average return
Figure 4.4 Probability of return within one standard deviation of the average return
Figure 4.5 Probability of return within two standard deviations of the average return
Figure 4.6 Probability of return within three standard deviations of the average return
Chapter 5: Introduction to Pricing and Valuation
Figure 5.1 Volatility term structure example
Figure 5.2 Volatility smile example
Figure 5.3 Volatility skew example
Figure 5.4 Volatility surface example
Chapter 7: The Binomial Option Pricing Model
Figure 7.1 Discrete points in time in one-, two-, three-, and four-period models
Figure 7.2 Characteristics of the underlying asset, one-period binomial model
Figure 7.3 Underlying asset example, one-period binomial model
Figure 7.4 Characteristics of a call option, one-period binomial model
Figure 7.5 Call option example, one-period binomial model
Figure 7.6 Cost and payoffs associated with a portfolio consisting of
α
of the underlying asset and a short call
Figure 7.7 Cost and payoffs example associated with a portfolio consisting of
α
of the underlying asset and a short call
Figure 7.8 Underlying asset example, two-period binomial model
Figure 7.9 European-style put option example, two-period binomial model
Figure 7.10 Midpoint node valuation, European-style put option example, two-period binomial model
Figure 7.11 Option valuation, European-style put option example, two-period binomial model
Figure 7.12 Option valuation, American-style put option example, two-period binomial model
Chapter 9: Understanding Delta and Gamma
Figure 9.1 Delta across the underlying asset price for long and short calls and puts
Figure 9.2 Gamma across the underlying asset price for long and short calls and puts
Chapter 10: Understanding Vega, Rho, and Theta
Figure 10.1 The symmetrical sensitivity of forward positions
Figure 10.2 The asymmetrical sensitivity of long calls and puts
Figure 10.3 The asymmetrical sensitivity of short calls and puts
Figure 10.4 Examples of long call and put values across time to expiration
Chapter 11: Price and Volatility Trading Strategies
Figure 11.1 Long and short straddles' P&L diagrams
Figure 11.2 Long and short strangles' P&L diagrams
Chapter 12: Synthetic, Protective, and Yield-Enhancing Trading Strategies
Figure 12.1 P&L diagrams for long and short synthetic forwards
Figure 12.2 P&L diagrams for long and short synthetic calls
Figure 12.3 P&L diagrams for long and short synthetic puts
Figure 12.4 P&L diagram for a collar
Chapter 13: Spread Trading Strategies
Figure 13.1 P&L diagrams for bull and bear spreads using calls
Figure 13.2 P&L diagrams for bull and bear spreads using puts
Figure 13.3 P&L diagram for a risk reversal
Figure 13.4 P&L diagrams for long and short butterfly spreads
Figure 13.5 P&L diagrams for long and short condor spreads
Chapter 14: Interest Rate Swaps
Figure 14.1 The exchange of fixed rate for floating rate in an interest rate swap
Figure 14.2 Floating rate borrower
Figure 14.3 Transformation of floating rate borrowing into fixed rate borrowing
Figure 14.4 Floating rate lender
Figure 14.5 Transformation of floating rate lending into fixed rate lending
Figure 14.6 Fixed rate borrower
Figure 14.7 Transformation of fixed rate borrowing into floating rate borrowing
Figure 14.8 Fixed rate lender
Figure 14.9 Transformation of a fixed rate lending into floating rate lending
Chapter 15: Credit Default Swaps, Cross-Currency Swaps, and Other Swaps
Figure 15.1 GBP borrower
Figure 15.2 Transformation of GBP borrowing into EUR borrowing: detailed cash flows
Figure 15.3 Transformation of GBP borrowing into EUR borrowing: net cash flows
List of Tables
Chapter 2: Call Options
Table 2.1 Call option exercise decision and long call payoff
Table 2.2 Call option exercise decision and long call payoff and P&L
Table 2.3 Call option exercise decision and short call payoff
Table 2.4 Call option exercise decision and short call payoff and P&L
Table 2.5 Long and short call P&L and net P&L
Table 2.6 Call option moneyness and long and short call payoff
Table 2.7 Comparison of forwards/futures and call option positions
Chapter 3: Put Options
Table 3.1 Put option exercise decision and long put payoff
Table 3.2 Put option exercise decision and long put payoff and P&L
Table 3.3 Put option exercise decision and short put payoff
Table 3.4 Put option exercise decision and short put payoff and P&L
Table 3.5 Long and short put P&L and net P&L
Table 3.6 Put option moneyness and long and short put payoff
Table 3.7 Comparison of forwards/futures, call option, and put option positions
Chapter 4: Useful Quantitative Concepts
Table 4.1 15-day sample
Table 4.2 Calculation of historical standard deviation
Chapter 5: Introduction to Pricing and Valuation
Table 5.1 Comparison of price and value concepts for forwards and options
Table 5.2 Option value calculation process
Table 5.3 Option value as the output of the Black-Scholes model
Table 5.4 Implied volatility as the output of the reverse-engineered Black-Scholes model
Chapter 6: Understanding Pricing and Valuation
Table 6.1 Learning objectives of each section of this chapter
Table 6.2 Review of payoff, price, and value equations
Table 6.3 Interest rate demanded as a function of the investor type and investment opportunity
Table 6.4 Probability and expected value concepts
Table 6.5 Interpretation of long call value
Table 6.6 Interpretation of long put value
Table 6.7 Interpretation of long forward value
Chapter 8: Introduction to the Greeks
Table 8.1 The Greeks as measures of sensitivity
Table 8.2 Source of sensitivity for each of the Greeks
Table 8.3 Equations for the Greeks
Table 8.4 Calculations of position value and the Greeks, long call example
Table 8.5 Summary of position value and Greeks, long call example
Table 8.6 Comparison of the Greeks to Black-Scholes model estimated changes
Chapter 9: Understanding Delta and Gamma
Table 9.1 Describing sensitivity using Delta and Gamma
Table 9.2 Delta and Gamma of forwards and options
Table 9.3 Example of Delta and Gamma for long and short forward and option positions
Table 9.4 The purchasing and selling counterparties in a forward, call, and put
Table 9.5 Delta across the underlying asset price
Table 9.6 Why Gamma is long, short, or neutral for each position
Table 9.7 Gamma across underlying asset prices
Chapter 10: Understanding Vega, Rho, and Theta
Table 10.1 Describing sensitivity using Vega, Rho, and Theta
Table 10.2 The Greeks of forwards and options
Table 10.3 Example of the Greeks for long and short forward and option positions
Table 10.4 The net impact of decreases in time to expiration
Chapter 11: Price and Volatility Trading Strategies
Table 11.1 Sensitivities and Greek positions that monetize price and volatility views
Table 11.2 Targeted Greek positions as function of price and volatility view combination
Table 11.3 Delta and Vega of forwards and options
Table 11.4 Forward and option positions that monetize price and volatility view combinations
Table 11.5 The Delta and Vega characteristics of long and short straddles
Table 11.6 ATM and ATM DNS
Table 11.7 Example of long straddle premiums, Delta and Vega
Table 11.8 Example of long straddle sensitivity
Table 11.9 Trading strategies through which to monetize price and volatility view combinations
Chapter 12: Synthetic, Protective, and Yield-Enhancing Trading Strategies
Table 12.1 Synthetic positions
Table 12.2 ATM, ATMF, and ATM DNS
Table 12.3 Option arbitrage
Chapter 14: Interest Rate Swaps
Table 14.1 The impact of the future level of LIBOR for interest rate swap counterparties
Table 14.2 LIBOR observations
Table 14.3 Calculation of floating leg payments
Table 14.4 Calculation of fixed leg payments
Table 14.5 Calculation of net cash flows
Table 14.6 Comparison of cash flow transformation strategies using interest rate swaps
Chapter 15: Credit Default Swaps, Cross-Currency Swaps, and Other Swaps
Table 15.1 Credit default swap sensitivity
Table 15.2 Exposure transformation strategies using credit default swaps
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.
Derivatives Essentials
An Introduction to Forwards,Futures, Options, and Swaps
ARON GOTTESMAN
Copyright © 2016 by Aron Gottesman. 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: Gottesman, Aron A., author.
Title: Derivatives essentials : An introduction to forwards, futures, options and swaps / Aron Gottesman.
Description: Hoboken : Wiley, 2016. | Series: Wiley finance | Includes index.
Identifiers: LCCN 2016014397 (print) | LCCN 2016016290 (ebook) | ISBN 9781119163497 (hardback) | ISBN 9781119163572 (ePDF) | ISBN 9781119163565 (ePub)
Subjects: LCSH: Derivative securities.
Classification: LCC HG6024.A3 G68 2016 (print) | LCC HG6024.A3 (ebook) | DDC 332.64/57—dc23
LC record available at https://lccn.loc.gov/2016014397
Cover Image: © hywards/Shutterstock
Cover design: Wiley
For my wife Ronit and our childrenLibby, Yakov, Raphi, Tzipora, and Kayla
Preface
This book provides an in-depth introduction to derivative securities. A derivative security is an agreement between two counterparties whose payoff depends on the value of an underlying asset. There is extensive interest in derivative securities due to their usefulness as tools through which investors can monetize views and transform exposures. Yet many that pursue an understanding of derivative securities can be frustrated with educational material that assumes the learner has sophisticated quantitative skills. Further, those with sophisticated quantitative skills can be frustrated with educational material that derives equations with little insight into the economic nature of derivative securities products and strategies.
This book focuses on helping you develop a meaningful understanding of derivative securities products and strategies and how to communicate your understanding both conceptually as well as through equations. You will learn about each product and strategy and the reasons for investing in them. You will learn about quantitative pricing and valuation models and will develop a deep understanding as to why the models represent price and value. You will learn of the great importance of the sensitivity measures known as the “Greeks” and learn how to use them to understand and characterize products and strategies.
Quantitative modeling is an important element of derivative securities, and this book will present quantitative models. However, this book does not assume that you have sophisticated quantitative or finance skills beyond the ability to add, subtract, multiply, divide, raise to a power, and rudimentary familiarity with time value of money concepts. Any other quantitative concept that is required to understand the material in this book will be introduced before it is required. Further, this book does not intend to provide comprehensive mathematical derivations nor provide quantitative overviews of each of the myriad of derivative securities variations in existence. Instead, the quantitative analysis in this book focuses on several key products through which we will explore conceptual and quantitative insights that are broadly applicable to other products and, most importantly, enable you to verbally communicate a deep understanding of products and strategies.
There are five parts to this book:
Part One
: Introduction to Forwards, Futures, and Options (
Chapters 1
–
3
)
Part Two
: Pricing and Valuation (
Chapters 4
–
7
)
Part Three
: The Greeks (
Chapters 8
–
10
)
Part Four
: Trading Strategies (
Chapters 11
–
13
)
Part Five
: Swaps (
Chapters 14
–
15
)
Part One introduces forwards, futures, and options. Forwards and futures are agreements that obligate counterparties to transact in the future. Options are agreements that provide one of the counterparties a right, and not an obligation, to transact in the future. In Part One you will learn about the key characteristics of forwards, futures, and options and each position's cash flows, payoffs, and P&L (profit and loss). You will also learn why forwards, futures, and options are described as zero-sum games and the concepts of moneyness and counterparty credit risk.
Part Two explores pricing and valuation of forwards and options. In Part Two you will learn to distinguish between price and value and explore models of price and value for each position, including the Black-Scholes and binomial option pricing models. You will also learn about the assumptions that these models make, risk-neutral valuation, and why the models represent price and value. You will also be introduced to the concepts of implied volatility and volatility surfaces.
Part Three explores the “Greeks,” which are measures of product and strategy sensitivity to change in the determinants of their value. In Part Three you will learn how to define, calculate, and interpret the Greeks and why they can be inaccurate. You will also develop a deep understanding of how the Greeks can be used to understand and describe sensitivity; why a given Greek will be positive, negative, or zero; and why its magnitude can change.
Part Four explores trading strategies. In Part Four you will learn how to describe and implement price and volatility trading strategies, create synthetic positions, and implement protective, yield enhancing, and spread trading strategies. The trading strategies that will be explored in Part Four include straddles, strangles, protective puts, covered calls, collars, bull spreads, bear spreads, risk reversals, butterfly spreads, and condor spreads, among others. You will also learn advanced concepts related to moneyness and put-call parity.
Part Five introduces swaps. A swap is an exchange of cash flows between two counterparties over a number of periods of time. In an interest rate swap the counterparties exchange fixed and floating interest rates. In a credit default swap periodic payments of spread are exchanged for a payment contingent on a credit event. In a cross-currency swap the counterparties exchange interest payments in different currencies. In Part Five you will learn about the key characteristics of these swaps, their sensitivities and cash flows, and how they can be used to transform exposures.
Most of the chapters in this book build on the material in previous chapters. It is therefore important that you truly understand each chapter before advancing to the next. To allow you to test your understanding, there are more than 650 Knowledge check questions throughout the book, the solutions to which are provided in the appendix. The Knowledge check questions can be used to ensure absorption of the material both when you learn the material for the first time and also when you review.
I hope this book provides you with a deep understanding of derivative securities and an enjoyable and valuable learning experience!
Acknowledgments
I want to acknowledge the contribution of Bill Falloon of John Wiley & Sons. This book would not have been brought to completion without Bill's critical support. I also want to acknowledge Meg Freeborn, Michael Henton, and Chaitanya Mella of Wiley, Kevin Mirabile of Fordham University, and my colleagues at Pace University including Niso Abuaf, Lew Altfest, Neil Braun, Arthur Centonze, Burcin Col, Ron Filante, Natalia Gershun, Elena Goldman, Iuliana Ismailescu, Padma Kadiyala, Maurice Larraine, Sophia Longman, Ray Lopez, Ed Mantell, Matt Morey, Jouahn Nam, Richard Ottoo, Joe Salerno, Michael Szenberg, Carmen Urma, PV Viswanath, Tom Webster, Berry Wilson, and Kevin Wynne. I also want to acknowledge Niall Darby, Stephen Feline, Allegra Kettelkamp, John O'Toole, Patrick Pancoast, Carlos Remigio, Lisa Ryan, and the entire team at Intuition. I further want to acknowledge Moshe Milevsky, Eli Prisman, and Gordon Roberts of York University and Gady Jacoby of the University of Manitoba who helped spark my career. Thank you to my many students from whom I've learned tremendously. Finally, thank you to my wife Ronit, a woman of valor, and our children Libby, Yakov, Raphi, Tzipora, and Kayla for providing so much love and support.
About the Author
Aron Gottesman is Professor of Finance and the Chair of the Department of Finance and Economics at the Lubin School of Business at Pace University in Manhattan. He holds a PhD in Finance, an MBA in Finance, and a BA in Psychology, all from York University. He has published articles in academic journals including the Journal of Financial Intermediation, Journal of Banking and Finance, Journal of Empirical Finance, and the Journal of Financial Markets, among others, and has coauthored several books. Aron Gottesman's research has been cited in newspapers and popular magazines, including The Wall Street Journal, The New York Times, Forbes Magazine, and Business Week. He teaches courses on derivative securities, financial markets, and asset management. Aron Gottesman also presents workshops to financial institutions. His website can be accessed at www.arongottesman.com.
Part One
Introduction to Forwards, Futures, and Options
Chapter 1Forwards and Futures
INTRODUCTION
A derivative security is an agreement between two counterparties whose payoff depends on the value of an underlying asset. In this chapter we will explore agreements that obligate counterparties to transact in the future, known as forward contracts and futures contracts.
After you read this chapter you will be able to
Describe the key characteristics of a forward.
Define and contrast the concepts of payoff and P&L.
Describe a forward's cash flows, payoff, and P&L.
Understand how equations and P&L diagrams can be used to describe a forward's cash flows.
Understand when forwards earn profits, suffer losses, and break even.
Explain why forwards are zero-sum games.
Define counterparty credit risk and understand mechanisms through which it is managed and minimized.
Describe futures contracts.
Compare and contrast forwards and futures.
1.1 FORWARD CONTRACT CHARACTERISTICS
A forward contract is an agreement between two counterparties that obligates them to transact in the future. The key characteristics of a forward are as follows:
One of the counterparties is referred to as the “long position” or “long forward,” and the other counterparty is referred to as the “short position” or “short forward.”
The long forward is obligated to purchase an asset from the short forward at a future point in time. The short forward is obligated to sell the asset.
The asset is known as the “underlying asset.” The underlying asset can be any asset. Common examples include stocks, bonds, currencies, and commodities.
The future point in time when the transaction occurs is known as the “expiration date.” For example, a forward may have an expiration date that is three months after initiation.
The price at which the underlying asset is purchased is called the “forward price.” The forward price is set at initiation though the transaction only takes place in the future. For example, at initiation two counterparties may agree to a forward price of $100 and an expiration date that is in three months. The long forward is obligated to purchase the asset from the short forward for $100 in three months.
All details are specified at initiation, including:
The counterparties
The underlying asset
The forward price
The expiration date
Hence, a forward is very similar to any transaction where an individual buys an asset from another individual, with the interesting twist that while the purchase price is set at initiation the transaction itself takes place at a future point in time. Figure 1.1 illustrates a forward.
Figure 1.1 Forward contract cash flows
For example, consider the following scenario:
Initiation = July 15
Expiration = September 15
Underlying asset = one share
Forward price = $100
Figure 1.2 illustrates this example.
Figure 1.2 Forward contract cash flows example
Figure 1.2 shows that at initiation, July 15, no transaction takes place. Instead, on July 15 the long forward and short forward enter into an agreement that
Obligates the long forward to purchase a single share from the short forward on September 15 for the forward price of $100. Hence, at expiration the long position pays $100 and receives one share in return.
Obligates the short forward to sell a single share to the long forward on September 15 for the forward price of $100. Hence at expiration the short forward receives $100 and delivers one share in return.
Let's consider another example:
Initiation = August 20
Expiration = December 20
Underlying asset = One ounce of gold
Forward price = $1,250
Figure 1.3 illustrates this example.
Figure 1.3 Forward contract cash flows example
Figure 1.3 shows that at initiation, August 20, no transaction takes place. However, on August 20 the long forward and short forward enter into an agreement that
Obligates the long forward to purchase one ounce of gold from the short forward on December 20 for the forward price of $1,250. Hence, at expiration the long forward pays $1,250 and receives one ounce of gold in return.
Obligates the short forward to sell one ounce of gold to the long forward on December 20 for the forward price of $1,250. Hence, at expiration the short forward receives $1,250 and delivers one ounce of gold in return.
Knowledge check
Q 1.1:
What is a “forward contract”?
Q 1.2:
What is the long forward position's obligation?
Q 1.3:
What is the short forward position's obligation?
Q 1.4:
What is the “expiration date”?
Q 1.5:
What is the “forward price”?
1.2 LONG FORWARD PAYOFF
Payoff is the cash flow that occurs at expiration. A long forward is obligated to purchase the asset through paying the forward price at expiration. Hence, the long forward's payoff is the value of the underlying asset that it receives at expiration minus the forward price it pays. The value of the underlying asset at expiration is its market price at that time.
The long forward's payoff can be positive, negative, or zero:
Positive payoff occurs when the price of the asset received is greater than the forward price paid.
Negative payoff occurs when the price of the asset received is less than the forward price paid.
Zero payoff occurs when the price of the asset received is equal to the forward price paid.
We can describe the long forward's payoff using an equation:
This equation can be restated using notation rather than words. Let's define the following notation:
T
=
Expiration date
=
Underlying asset price at time
T
F
=
Forward price
With this notation, we can rewrite the equation for the long forward's payoff:
For example, consider the following scenario:
Initiation = June 1
Expiration = July 1
Forward price = $180
Underlying asset price on July 1 = $200
This scenario is illustrated in Figure 1.4.
Figure 1.4 Long forward payoff example
In this example, the long forward's payoff is:
Knowledge check
Q 1.6:
What is “payoff”?
Q 1.7:
What is the long forward's payoff?
Q 1.8:
When does the long forward have a positive payoff?
Q 1.9:
When does the long forward have a negative payoff?
Q 1.10:
When does the long forward have zero payoff?
1.3 LONG FORWARD P&L
P&L is profit and loss. The distinction between payoff and P&L is as follows:
Payoff: The cash flow that occurs at expiration
P&L: The difference between the cash flows at initiation and expiration
Hence, P&L takes into account any cash flow that is paid or received at initiation.
A long forward's payoff and P&L are identical. After all, the long forward does not pay nor receive a cash flow at initiation. The equation for a long forward's P&L is therefore identical to the equation for the long forward's payoff:
The long forward may experience a profit, suffer a loss, or break even:
Profit occurs when the price of the asset received is greater than the forward price paid.
Loss occurs when the price of the asset received is less than the forward price paid.
Breakeven occurs when the price of the asset received is equal to the forward price paid.
We can describe the long forward's breakeven point using an equation:
For example, consider the following scenario:
Initiation = May 10
Expiration = July 15
Forward price = $1,500
Underlying asset price on July 15 = $1,250
This scenario is illustrated in Figure 1.5.
Figure 1.5 Long forward P&L example
In this example, the long forward's P&L is:
Knowledge check
Q 1.11:
What is “P&L”?
Q 1.12:
What is the long forward's P&L?
Q 1.13:
When does the long forward earn a profit?
Q 1.14:
When does the long forward suffer a loss?
Q 1.15:
When does the long forward break even?
1.4 SHORT FORWARD PAYOFF
A short forward is obligated to sell an asset at expiration in return for which it receives the forward price. Hence, the short forward's payoff at expiration is the forward price received minus the price of the asset it delivers. The short forward's payoff can be positive, negative, or zero:
Positive payoff occurs when the forward price received is greater than the price of the asset delivered.
Negative payoff occurs when the forward price received is less than the price of the asset delivered.
Zero payoff occurs when the forward price received is equal to the price of the asset delivered.
The short forward's payoff can be expressed as:
For example, consider the following scenario:
Initiation = October 3
Expiration = February 1
Forward price = $65
Underlying asset price on February 1 = $82
This scenario is illustrated inFigure 1.6.
Figure 1.6 Short forward payoff example
In this example, the short forward's payoff is:
Knowledge check
Q 1.16:
What is the short forward's payoff?
Q 1.17:
When does the short forward have a positive payoff?
Q 1.18:
When does the short forward have a negative payoff?
Q 1.19:
When does the short forward have zero payoff?
1.5 SHORT FORWARD P&L
P&L is the difference between the cash flows that occur at initiation and expiration. A short forward's P&L is equal to its payoff as the only cash flow associated with a short forward is the payoff that takes place at expiration. Therefore, the equation for the short forward's P&L is identical to the equation for the short forward's payoff:
The short forward may experience a profit, suffer a loss, or break even:
Profit occurs when the forward price received is greater than the price of the asset delivered.
Loss occurs when the forward price received is less than the price of the asset delivered.
Breakeven occurs when the forward price received is equal to the price of the asset delivered.
We can describe the short forward's breakeven point using an equation:
The short forward's breakeven point is identical to the long forward's breakeven point.
For example, consider the following scenario:
Initiation = May 21
Expiration = June 3
Forward price = $140,000
Underlying asset price on June 3 = $130,000
This scenario is illustrated in Figure 1.7.
Figure 1.7 Short forward P&L example
In this example, the short forward's P&L is:
Knowledge check
Q 1.20:
What is the short forward's P&L?
Q 1.21:
When does the short forward earn a profit?
Q 1.22:
When does the short forward suffer a loss?
Q 1.23:
When does the short forward break even?
1.6 LONG FORWARD P&L DIAGRAM
A P&L diagram, such as the one in Figure 1.8, illustrates the P&L associated with a long forward as a function of the underlying asset price at expiration.
Figure 1.8 Long forward P&L diagram
The P&L diagram in Figure 1.8 consists of two axes: The horizontal (left to right) axis represents the underlying asset price at expiration, ST. The lowest possible underlying asset price is zero. The vertical (top to bottom) axis represents P&L.
The upward sloping diagonal (bottom-left to top-right) line represents the P&L as a function of the underlying asset price. P&L depends on the underlying asset price:
If the underlying asset price is less than the forward price, then the P&L is negative and the long forward suffers a loss.
If the underlying asset price is greater than the forward price, then the P&L is positive and the long forward earns a profit.
If the underlying asset price is equal to the forward price, then the P&L is zero and the long forward is at its breakeven point.
For example, consider the following scenario:
Initiation = June 1
Expiration = July 1
Forward price = $75
On June 1 we do not know what the underlying asset price will be on July 1. The P&L diagram in Figure 1.9 depicts the range of potential P&L that the long forward may experience on July 1. The potential payoffs will depend on the value of the underlying asset price on July 1. If the underlying asset price is greater than the forward price of $75, then the P&L will be positive. If the underlying asset price is less than $75, then the P&L will be negative. If the underlying asset price is $75, then the P&L will be zero.
Figure 1.9 Long forward P&L diagram
Knowledge check
Q 1.24:
What does the horizontal axis of a P&L diagram represent?
Q 1.25:
What does the vertical axis of a P&L diagram represent?
Q 1.26:
What does a long forward's P&L diagram look like?
Q 1.27:
What is the positive P&L range for the long forward?
Q 1.28:
What is the negative P&L range for the long forward?
1.7 SHORT FORWARD P&L DIAGRAM
Figure 1.10 presents the P&L diagram for a short forward position.
Figure 1.10 Short forward P&L diagram
The axes associated with the short forward's P&L diagram in Figure 1.10 are identical to the axes used for the long forward's P&L diagram in Figure 1.8. The horizontal axis represents the underlying asset price at expiration. The vertical axis represents P&L. The downward sloping diagonal line (top-left to bottom-right) represents the short forward's P&L, which depends on the underlying asset price:
If the underlying asset price is less than the forward price, then the P&L is positive and the short forward earns a profit.
If the underlying asset price is greater than the forward price, then the P&L is negative and the short forward suffers a loss.
If the underlying asset price is equal to the forward price, then the P&L is zero and the short forward is at its breakeven point.
The short forward's breakeven point is identical to the long forward's breakeven point. For the long forward the breakeven point is the point where, as the underlying asset price increases, the long forward switches from loss to profit, while for the short forward the breakeven point is the point where it switches from profit to loss.
For example, consider the following scenario:
Initiation = December 1
Expiration = January 12
Forward price = $60
On December 1 we do not know what the underlying asset price will be on January 12. The P&L diagram in Figure 1.11 depicts the range of potential P&L that the short forward may experience on January 12. The potential payoffs will depend on the underlying asset price on January 12. If the underlying asset price is less than $60, then the P&L will be positive. If the underlying asset price is greater than $60, then the P&L will be negative. If the underlying asset price is $60, then the P&L will be zero.
Figure 1.11 Short forward P&L diagram
Knowledge check
Q 1.29:
What does a short forward's P&L diagram look like?
Q 1.30:
What is the positive P&L range for the short forward?
Q 1.31:
What is the negative P&L range for the short forward?
1.8 FORWARDS ARE ZERO-SUM GAMES
Forwards are zero-sum games. This means that any profit that one of the counterparties receives is exactly equal to the loss that the other counterparty suffers. This is evident from the P&L associated with long and short forwards:
The net of the P&L across the two counterparties is:
This can also be illustrated through observing that the P&L diagrams for long and short forwards are mirror images of each other, as shown in Figure 1.12. Clearly, the net P&L is zero.
Figure 1.12 Forward contract as a zero-sum game
For example, consider the following scenario:
Forward price = $180
Underlying asset price at expiration = $197.5
The long and short forward P&Ls are:
The net P&L across the long and short forwards is:
Knowledge check
Q 1.32:
What is a “zero-sum game”?
Q 1.33:
Why is a forward a zero-sum game?
1.9 COUNTERPARTY CREDIT RISK
An investor that enters into either a long or short forward has an obligation that it must satisfy:
The long forward is obligated to purchase an asset from the short forward in the future.
The short forward is obligated to sell an asset to the long forward in the future.
Each of the counterparties must fulfill its obligation whether it results in a positive or negative payoff. A counterparty that has earned a positive payoff is relying on the other counterparty to fulfill its obligation. Should the other counterparty fail to do so, the counterparty that has earned the positive payoff will lose the payoff and therefore suffer a loss. The risk of suffering a loss because one's counterparty does not fulfill its obligations is called “counterparty credit risk.”
For example, consider the following forward:
