Derivatives Essentials

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Preface xiii Acknowledgements xvii About the Author xix PART ONE Introduction to Forwards, Futures, and Options CHAPTER 1 Forwards and Futures 3 1.1 Forward contract characteristics 3 1.2 Long forward payoff 6 1.3 Long forward P&L 8 1.4 Short forward payoff 9 1.5 Short forward P&L 10 1.6 Long forward P&L diagram 12 1.7 Short forward P&L diagram 13 1.8 Forwards are zero-sum games 15 1.9 Counterparty credit risk 17 1.10 Futures contracts 19 CHAPTER 2 Call Options 22 2.1 Call option characteristics 22 2.2 Long call payoff 25 2.3 Long call P&L 27 2.4 Short call payoff 29 2.5 Short call P&L 30 2.6 Long call P&L diagram 32 2.7 Short call P&L diagram 33 2.8 Call options are zero-sum games 35 2.9 Call option moneyness 37 2.10 Exercising a call option early 38 2.11 Comparison of call options and forwards/futures 40 CHAPTER 3 Put Options 44 3.1 Put option characteristics 44 3.2 Long put payoff 47 3.3 Long put P&L 49 3.4 Short put payoff 50 3.5 Short put P&L 52 3.6 Long put P&L diagram 53 3.7 Short put P&L diagram 55 3.8 Put options are zero-sum games 57 3.9 Put option moneyness 58 3.10 Exercising a put option early 59 3.11 Comparison of put options, call options, and forwards/futures 60 PART TWO Pricing and Valuation CHAPTER 4 Useful Quantitative Concepts 65 4.1 Compounding conventions 66 4.2 Calculating future value and present value 68 4.3 Identifying continuously compounded interest rates 71 4.4 Volatility and historical standard deviation 72 4.5 Interpretation of standard deviation 77 4.6 Annualized standard deviation 80 4.7 The standard normal cumulative distribution function 81 4.8 The z-score 83 CHAPTER 5 Introduction to Pricing and Valuation 86 5.1 The concepts of price and value of a forward contract 87 5.2 The concepts of price and value of an option 88 5.3 Comparison of price and value concepts for forwards and options 90 5.4 Forward value 91 5.5 Forward price 92 5.6 Option value: The Black-Scholes model 94 5.7 Calculating the Black-Scholes model 96 5.8 Black-Scholes model assumptions 98 5.9 Implied volatility 99 CHAPTER 6 Understanding Pricing and Valuation 105 6.1 Review of payoff, price, and value equations 106 6.2 Value as the present value of expected payoff 108 6.3 Risk-neutral valuation 109 6.4 Probability and expected value concepts 112 6.5 Understanding the Black-Scholes equation for call value 117 6.6 Understanding the Black-Scholes equation for put value 120 6.7 Understanding the equation for forward value 122 6.8 Understanding the equation for forward price 123 CHAPTER 7 The Binomial Option Pricing Model 126 7.1 Modeling discrete points in time 126 7.2 Introduction to the one-period binomial option pricing model 127 7.3 Option valuation, one-period binomial option pricing model 131 7.4 Two-period binomial option pricing model, European-style option 135 7.5 Two-period binomial model, American-style option 138 7.6 Multi-period binomial option pricing models 140 PART THREE The Greeks CHAPTER 8 Introduction to the Greeks 145 8.1 Definitions of the Greeks 146 8.2 Characteristics of the Greeks 146 8.3 Equations for the Greeks 149 8.4 Calculating the Greeks 151 8.5 Interpreting the Greeks 153 8.6 The accuracy of the Greeks 156 CHAPTER 9 Understanding Delta and Gamma 158 9.1 Describing sensitivity using Delta and Gamma 158 9.2 Understanding Delta 161 9.3 Delta across the underlying asset price 162 9.4 Understanding Gamma 166 9.5 Gamma across the underlying asset price 167 CHAPTER 10 Understanding Vega, Rho, and Theta 171 10.1 Describing sensitivity using Vega, Rho, and Theta 171 10.2 Understanding Vega 174 10.3 Understanding Rho 177 10.4 Understanding Theta 178 PART FOUR Trading Strategies CHAPTER 11 Price and Volatility Trading Strategies 189 11.1 Price and volatility views 189 11.2 Relating price and volatility views to Delta and Vega 191 11.3 Using forwards, calls, and puts to monetize views 193 11.4 Introduction to straddles 194 11.5 Delta and Vega characteristics of long and short straddles 195 11.6 The ATM DNS strike price 196 11.7 Straddle: numerical example 197 11.8 P&L diagrams for long and short straddles 199 11.9 Breakeven points for long and short straddles 199 11.10 Introduction to strangles 201 11.11 P&L diagrams for long and short strangles 202 11.12 Breakeven points for long and short strangles 202 11.13 Summary of simple price and volatility trading strategies 204 CHAPTER 12 Synthetic, Protective, and Yield-Enhancing Trading Strategies 206 12.1 Introduction to put-call parity and synthetic positions 207 12.2 P&L diagrams of synthetic positions 208 12.3 Synthetic positions premiums and ATMF 212 12.4 The Greeks of synthetic positions 214 12.5 Option arbitrage 215 12.6 Protective puts 217 12.7 Covered calls 218 12.8 Collars 219 CHAPTER 13 Spread Trading Strategies 223 13.1 Bull and bear spreads using calls 223 13.2 Bull and bear spreads using puts 226 13.3 Risk reversals 229 13.4 Butterfly spreads 232 13.5 Condor spreads 236 PART FIVE Swaps CHAPTER 14 Interest Rate Swaps 243 14.1 Interest rate swap characteristics 243 14.2 Interest rate swap cash flows 246 14.3 Calculating interest rate swap cash flows 249 14.4 How interest rate swaps can transform cash flows 256 CHAPTER 15 Credit Default Swaps, Cross-Currency Swaps, and Other Swaps 264 15.1 Credit default swap characteristics 264 15.2 Key determinants of the credit default swap spread 267 15.3 Cross-currency swap characteristics 270 15.4 Transforming cash flows using a cross-currency swap 270 15.5 Other swap varieties 273 Appendix: Solutions to Knowledge Check Questions 275 Index 301

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. He teaches courses on derivative securities, financial markets, and asset management, and presents corporate workshops on derivative securities to bulge bracket financial institutions.

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