Table of Contents

Preface

Acknowledgments

About the Author

Part One: Introduction to Forwards, Futures, and Options

Chapter 1: Forwards and Futures
1. Introduction
2. 1.1 Forward contract characteristics
3. 1.2 Long forward payoff
4. 1.3 Long forward P&L
5. 1.4 Short forward payoff
6. 1.5 Short forward P&L
7. 1.6 Long forward P&L diagram
8. 1.7 Short forward P&L diagram
9. 1.8 Forwards are zero-sum games
10. 1.9 Counterparty credit risk
11. 1.10 Futures contracts
12. Key Points
Chapter 2: Call Options
1. Introduction
2. 2.1 Call option characteristics
3. 2.2 Long call payoff
4. 2.3 Long call P&L
5. 2.4 Short call payoff
6. 2.5 Short call P&L
7. 2.6 Long call P&L diagram
8. 2.7 Short call P&L diagram
9. 2.8 Call options are zero-sum games
10. 2.9 Call option moneyness
11. 2.10 Exercising a call option early
12. 2.11 Comparison of call options and forwards/futures
13. Key Points
Chapter 3: Put Options
1. Introduction
2. 3.1 Put option characteristics
3. 3.2 Long put payoff
4. 3.3 Long put P&L
5. 3.4 Short put payoff
6. 3.5 Short put P&L
7. 3.6 Long put P&L diagram
8. 3.7 Short put P&L diagram
9. 3.8 Put options are zero-sum games
10. 3.9 Put option moneyness
11. 3.10 Exercising a put option early
12. 3.11 Comparison of put options, call options, and forwards
13. Key Points

Part Two: Pricing and Valuation

Chapter 4: Useful Quantitative Concepts
1. Introduction
2. 4.1 Compounding conventions
3. 4.2 Calculating future value and present value
4. 4.3 Identifying continuously compounded interest rates
5. 4.4 Volatility and historical standard deviation
6. 4.5 Interpretation of standard deviation
7. 4.6 Annualized standard deviation
8. 4.7 The standard normal cumulative distribution function
9. 4.8 The z-score
10. Key Points
Chapter 5: Introduction to Pricing and Valuation
1. Introduction
2. 5.1 The concepts of price and value of a forward contract
3. 5.2 The concepts of price and value of an option
4. 5.3 Comparison of price and value concepts for forwards and options
5. 5.4 Forward value
6. 5.5 Forward price
7. 5.6 Option value: The Black-Scholes model
8. 5.7 Calculating the Black-Scholes model
9. 5.8 Black-Scholes model assumptions
10. 5.9 Implied volatility
11. Key Points
Chapter 6: Understanding Pricing and Valuation
1. Introduction
2. 6.1 Review of payoff, price, and value equations
3. 6.2 Value as the present value of expected payoff
4. 6.3 Risk-neutral valuation
5. 6.4 Probability and expected value concepts
6. 6.5 Understanding the Black-Scholes equation for call value
7. 6.6 Understanding the Black-Scholes equation for put value
8. 6.7 Understanding the equation for forward value
9. 6.8 Understanding the equation for forward price
10. Key Points
Chapter 7: The Binomial Option Pricing Model
1. Introduction
2. 7.1 Modeling discrete points in time
3. 7.2 Introduction to the one-period binomial option pricing model
4. 7.3 Option valuation, one-period binomial option pricing model
5. 7.4 Two-period binomial option pricing model, European-style option
6. 7.5 Two-period binomial model, American-style option
7. 7.6 Multi-period binomial option pricing models
8. Key Points

Part Three: The Greeks

Chapter 8: Introduction to the Greeks
1. Introduction
2. 8.1 Definitions of the Greeks
3. 8.2 Characteristics of the Greeks
4. 8.3 Equations for the Greeks
5. 8.4 Calculating the Greeks
6. 8.5 Interpreting the Greeks
7. 8.6 The accuracy of the Greeks
8. Key Points
Chapter 9: Understanding Delta and Gamma
1. Introduction
2. 9.1 Describing sensitivity using Delta and Gamma
3. 9.2 Understanding Delta
4. 9.3 Delta across the underlying asset price
5. 9.4 Understanding Gamma
6. 9.5 Gamma across the underlying asset price
7. Key Points
Chapter 10: Understanding Vega, Rho, and Theta
1. Introduction
2. 10.1 Describing sensitivity using Vega, Rho, and Theta
3. 10.2 Understanding Vega
4. 10.3 Understanding Rho
5. 10.4 Understanding Theta
6. Key Points

Part Four: Trading Strategies

Chapter 11: Price and Volatility Trading Strategies
1. Introduction
2. 11.1 Price and volatility views
3. 11.2 Relating price and volatility views to Delta and Vega
4. 11.3 Using forwards, calls, and puts to monetize views
5. 11.4 Introduction to straddles
6. 11.5 Delta and Vega characteristics of long and short straddles
7. 11.6 The ATM DNS strike price
8. 11.7 Straddle: numerical example
9. 11.8 P&L diagrams for long and short straddles
10. 11.9 Breakeven points for long and short straddles
11. 11.10 Introduction to strangles
12. 11.11 P&L diagrams for long and short strangles
13. 11.12 Breakeven points for long and short strangles
14. 11.13 Summary of simple price and volatility trading strategies
15. Key Points
Chapter 12: Synthetic, Protective, and Yield-Enhancing Trading Strategies
1. Introduction
2. 12.1 Introduction to put-call parity and synthetic positions
3. 12.2 P&L diagrams of synthetic positions
4. 12.3 Synthetic positions premiums and ATMF
5. 12.4 The Greeks of synthetic positions
6. 12.5 Option arbitrage
7. 12.6 Protective puts
8. 12.7 Covered calls
9. 12.8 Collars
10. Key Points
Chapter 13: Spread Trading Strategies
1. Introduction
2. 13.1 Bull and bear spreads using calls
3. 13.2 Bull and bear spreads using puts
4. 13.3 Risk reversals
5. 13.4 Butterfly spreads
6. 13.5 Condor spreads
7. Key Points

Part Five: Swaps

Chapter 14: Interest Rate Swaps
1. Introduction
2. 14.1 Interest rate swap characteristics
3. 14.2 Interest rate swap cash flows
4. 14.3 Calculating interest rate swap cash flows
5. 14.4 How interest rate swaps can transform cash flows
6. Key Points
Chapter 15: Credit Default Swaps, Cross-Currency Swaps, and Other Swaps
1. Introduction
2. 15.1 Credit default swap characteristics
3. 15.2 Key determinants of the credit default swap spread
4. 15.3 Cross-currency swap characteristics
5. 15.4 Transforming cash flows using a cross-currency swap
6. 15.5 Other swap varieties
7. 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

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

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Published simultaneously in Canada.

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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 design: Wiley

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.

Derivatives Essentials

An Introduction to Forwards,
Futures, Options, and Swaps

Preface

Acknowledgments

About the Author

Part One

Introduction to Forwards, Futures, and Options