Exotic Options and Hybrids: A Guide to Structuring, Pricing and Trading(The Wiley Finance Series)

The recent financial crisis brought to light many of the misunderstandings and misuses of exotic derivatives. With market participants on both the buy and sell-side having been found guilty of not understanding the products they were dealing with, never before has there been a greater need for clarification and explanation. Exotic Options and Hybrids is a practical guide to structuring, pricing and hedging complex exotic options and hybrid derivatives that will serve readers through the recent crisis, the road to recovery, the next bull market and beyond. Written by experienced practitioners, it focuses on the three main parts of a derivative’s life: the structuring of a product, its pricing and its hedging. Divided into four parts, the book covers a multitude of structures, encompassing many of the most up-to-date and promising products from exotic equity derivatives and structured notes to hybrid derivatives and dynamic strategies. Based on a realistic setting from the heart of the business, inside a derivatives operation, the practical and intuitive discussions of these aspects make these exotic concepts truly accessible. Adoptions of real trades are examined in detail, and all of the numerous examples are carefully selected so as to highlight interesting and significant aspects of the business. The introduction of payoff structures is accompanied by scenario analysis, diagrams and lifelike sample term sheets. Readers learn how to spot where the risks lie to pave the way for sound valuation and hedging of such products. There are also questions and accompanying discussions dispersed in the text, each exploited to illustrate one or more concepts from the context in which they are set. The applications, the strengths and the limitations of various models are highlighted, in relevance to the products and their risks, rather than the model implementations. Models are de-mystified in separately dedicated sections, but their implications are alluded to throughout the book in an intuitive and non-mathematical manner. By discussing exotic options and hybrids in a practical, non-mathematical and highly intuitive setting, this book will blast through the misunderstanding of exotic derivatives, enabling practitioners to fully understand and correctly structure, price and hedge theses products effectively, and stand strong as the only book in its class to make these “exotic” concepts truly accessible.

Table of Contents:
List of Symbols and Abbreviations xvii Preface xix Part I Foundations 1 1 Basic Instruments 3 1.1 Introduction 3 1.2 Interest Rates 3 1.2.1 LIBOR vs Treasury Rates 4 1.2.2 Yield Curves 4 1.2.3 Time Value of Money 5 1.2.4 Bonds 6 1.2.5 Zero Coupon Bonds 7 1.3 Equities and Currencies 8 1.3.1 Stocks 8 1.3.2 Foreign Exchange 10 1.3.3 Indices 10 1.3.4 Exchange-traded Funds 11 1.3.5 Forward Contracts 11 1.3.6 Futures 12 1.4 Swaps 13 1.4.1 Interest Rate Swaps 13 1.4.2 Cross-currency Swaps 14 1.4.3 Total Return Swaps 16 1.4.4 Asset Swaps 16 1.4.5 Dividend Swaps 16 2 The World of Structured Products 19 2.1 The Products 19 2.1.1 The Birth of Structured Products 19 2.1.2 Structured Product Wrappers 20 2.1.3 The Structured Note 20 2.2 The Sell Side 21 2.2.1 Sales and Marketing 21 2.2.2 Traders and Structurers 22 2.3 The Buy Side 23 2.3.1 Retail Investors 23 2.3.2 Institutional Investors 24 2.3.3 Bullish vs Bearish, the Economic Cycle 24 2.3.4 Credit Risk and Collateralized Lines 25 2.4 The Market 26 2.4.1 Issuing a Structured Product 26 2.4.2 Liquidity and a Two-way Market 27 2.5 Example of an Equity Linked Note 28 3 Vanilla Options 31 3.1 General Features of Options 31 3.2 Call and Put Option Payoffs 32 3.3 Put–call Parity and Synthetic Options 34 3.4 Black–Scholes Model Assumptions 35 3.4.1 Risk-neutral Pricing 36 3.5 Pricing a European Call Option 37 3.6 Pricing a European Put Option 38 3.7 The Cost of Hedging 40 3.8 American Options 42 3.9 Asian Options 43 3.10 An Example of the Structuring Process 44 3.10.1 Capital Protection and Equity Participation 44 3.10.2 Capital at Risk and Higher Participation 46 4 Volatility, Skew and Term Structure 49 4.1 Volatility 49 4.1.1 Realized Volatility 49 4.1.2 Implied Volatility 51 4.2 The Volatility Surface 52 4.2.1 The Implied Volatility Skew 52 4.2.2 Term Structure of Volatilities 56 4.3 Volatility Models 57 4.3.1 Model Choice and Model Risk 57 4.3.2 Black–Scholes or Flat Volatility 58 4.3.3 Local Volatility 60 4.3.4 Stochastic Volatility 62 5 Option Sensitivities: Greeks 65 5.1 Delta 66 5.2 Gamma 72 5.3 Vega 74 5.4 Theta 76 5.5 Rho 77 5.6 Relationships between the Greeks 78 5.7 Volga and Vanna 80 5.7.1 Vega–Gamma (Volga) 80 5.7.2 Vanna 81 5.8 Multi-asset Sensitivities 81 5.9 Approximations to Black–Scholes and Greeks 82 6 Strategies Involving Options 87 6.1 Traditional Hedging Strategies 87 6.1.1 Protective Puts 87 6.1.2 Covered Calls 89 6.2 Vertical Spreads 90 6.2.1 Bull Spreads 90 6.2.2 Bear Spreads 93 6.3 Other Spreads 96 6.3.1 Butterfly Spreads 96 6.3.2 Condor Spreads 98 6.3.3 Ratio Spreads 99 6.3.4 Calendar Spreads 99 6.4 Option Combinations 100 6.4.1 Straddles 100 6.4.2 Strangles 101 6.5 Arbitrage Freedom of the Implied Volatility Surface 102 7 Correlation 105 7.1 Multi-asset Options 105 7.2 Correlation: Measurements and Interpretation 106 7.2.1 Realized Correlation 106 7.2.2 Correlation Matrices 109 7.2.3 Portfolio Variance 110 7.2.4 Implied Correlation 111 7.2.5 Correlation Skew 113 7.3 Basket Options 114 7.4 Quantity Adjusting Options: “Quantos” 116 7.4.1 Quanto Payoffs 116 7.4.2 Quanto Correlation and Quanto Option Pricing 116 7.4.3 Hedging Quanto Risk 117 7.5 Trading Correlation 118 7.5.1 Straddles: Index versus Constituents 118 7.5.2 Correlation Swaps 118 Part II Exotic Derivatives and Structured Products 121 8 Dispersion 123 8.1 Measures of Dispersion and Interpretations 123 8.2 Worst-of Options 125 8.2.1 Worst-of Call 125 8.2.2 Worst-of Put 127 8.2.3 Market Trends in Worst-of Options 128 8.3 Best-of options 129 8.3.1 Best-of Call 129 8.3.2 Best-of Put 131 8.3.3 Market Trends in Best-of Options 132 9 Dispersion Options 135 9.1 Rainbow Options 135 9.1.1 Payoff Mechanism 135 9.1.2 Risk Analysis 136 9.2 Individually Capped Basket Call (ICBC) 137 9.2.1 Payoff Mechanism 137 9.2.2 Risk Analysis 138 9.3 Outperformance Options 141 9.3.1 Payoff Mechanism 141 9.3.2 Risk Analysis 142 9.4 Volatility Models 143 10 Barrier Options 145 10.1 Barrier Option Payoffs 145 10.1.1 Knock-out Options 145 10.1.2 Knock-in Options 148 10.1.3 Summary 150 10.2 Black–Scholes Valuation 151 10.2.1 Parity Relationships 151 10.2.2 Closed Formulas for Continuously Monitored Barriers 151 10.2.3 Adjusting for Discrete Barriers 154 10.3 Hedging Down-and-in Puts 155 10.3.1 Monitoring the Barrier 155 10.3.2 Volatility and Down-and-in Puts 157 10.3.3 Dispersion Effect on Worst-of Down-and-in Puts 158 10.4 Barriers in Structured Products 160 10.4.1 Multi-asset Shark 160 10.4.2 Single Asset Reverse Convertible 163 10.4.3 Worst-of Reverse Convertible 164 11 Digitals 167 11.1 European Digitals 167 11.1.1 Digital Payoffs and Pricing 167 11.1.2 Replicating a European Digital 169 11.1.3 Hedging a Digital 169 11.2 American Digitals 172 11.3 Risk Analysis 174 11.3.1 Single Asset Digitals 174 11.3.2 Digital Options with Dispersion 176 11.3.3 Volatility Models for Digitals 177 11.4 Structured Products Involving European Digitals 178 11.4.1 Strip of Digitals Note 178 11.4.2 Growth and Income 179 11.4.3 Bonus Steps Certificate 181 11.5 Structured Products Involving American Digitals 183 11.5.1 Wedding Cake 183 11.5.2 Range Accrual 184 11.6 Outperformance Digital 185 11.6.1 Payoff Mechanism 185 11.6.2 Correlation Skew and Other Risks 186 12 Autocallable Structures 187 12.1 Single Asset Autocallables 187 12.1.1 General Features 187 12.1.2 Interest Rate/Equity Correlation 190 12.2 Autocallable Participating Note 192 12.3 Autocallables with Down-and-in Puts 194 12.3.1 Adding the Put Feature 194 12.3.2 Twin-Wins 194 12.3.3 Autocallables with Bonus Coupons 196 12.4 Multi-asset Autocallables 198 12.4.1 Worst-of Autocallables 198 12.4.2 Snowball Effect and Worst-of put Feature 200 12.4.3 Outperformance Autocallables 202 Part III More on Exotic Structures 205 13 The Cliquet Family 207 13.1 Forward Starting Options 207 13.2 Cliquets with Local Floors and Caps 208 13.2.1 Payoff Mechanism 209 13.2.2 Forward Skew and Other Risks 210 13.3 Cliquets with Global Floors and Caps 210 13.3.1 Vega Convexity 213 13.3.2 Levels of These Risks 215 13.4 Reverse Cliquets 217 14 More Cliquets and Related Structures 219 14.1 Other Cliquets 219 14.1.1 Digital Cliquets 219 14.1.2 Bearish Cliquets 220 14.1.3 Variable Cap Cliquets 221 14.1.4 Accumulators/Lock-in Cliquets 222 14.1.5 Replacement Cliquets 222 14.2 Multi-asset Cliquets 224 14.2.1 Multi-asset Cliquet Payoffs 224 14.2.2 Multi-asset Cliquet Risks 225 14.3 Napoleons 226 14.3.1 The Napoleon Structure 226 14.3.2 The Bearish Napoleon 227 14.4 Lookback Options 227 14.4.1 The Various Lookback Payoffs 227 14.4.2 Hedging Lookbacks 228 14.4.3 Sticky Strike and Sticky Delta 229 14.4.4 Skew Risk in Lookbacks 229 15 Mountain Range Options 231 15.1 Altiplano 231 15.2 Himalaya 233 15.3 Everest 235 15.4 Kilimanjaro Select 236 15.5 Atlas 238 15.6 Pricing Mountain Range Products 239 16 Volatility Derivatives 243 16.1 The Need for Volatility Derivatives 243 16.2 Traditional Methods for Trading Volatility 243 16.3 Variance Swaps 244 16.3.1 Payoff Description 245 16.3.2 Variance vs Volatility Swaps 246 16.3.3 Replication and Pricing of Variance Swaps 246 16.3.4 Capped Variance Swaps 248 16.3.5 Forward Starting Variance Swaps 249 16.3.6 Variance Swap Greeks 249 16.4 Variations on Variance Swaps 250 16.4.1 Corridor Variance Swaps 250 16.4.2 Conditional Variance Swaps 251 16.4.3 Gamma Swaps 253 16.5 Options on Realized Variance 254 16.6 The VIX: Volatility Indices 254 16.6.1 Options on the VIX 255 16.6.2 Combining Equity and Volatility Indices 256 16.7 Variance Dispersion 256 Part IV Hybrid Derivatives and Dynamic Strategies 259 17 Asset Classes (I) 261 17.1 Interest Rates 262 17.1.1 Forward Rate Agreements 262 17.1.2 Constant Maturity Swaps 263 17.1.3 Bonds 264 17.1.4 Yield Curves 265 17.1.5 Zero Coupon, LIBOR and Swap Rates 267 17.1.6 Interest Rate Swaptions 268 17.1.7 Interest Rate Caps and Floors 269 17.1.8 The SABR Model 270 17.1.9 Exotic Interest Rate Structures 271 17.2 Commodities 272 17.2.1 Forward and Futures Curves, Contango and Backwardation 273 17.2.2 Commodity Vanillas and Skew 276 18 Asset Classes (II) 279 18.1 Foreign Exchange 279 18.1.1 Forward and Futures Curves 279 18.1.2 FX Vanillas and Volatility Smiles 281 18.1.3 FX Implied Correlations 287 18.1.4 FX Exotics 287 18.2 Inflation 288 18.2.1 Inflation and the Need for Inflation Products 289 18.2.2 Inflation Swaps 289 18.2.3 Inflation Bonds 290 18.2.4 Inflation Derivatives 290 18.3 Credit 291 18.3.1 Bonds and Default Risk 292 18.3.2 Credit Default Swaps 293 19 Structuring Hybrid Derivatives 295 19.1 Diversification 295 19.1.1 Multi-asset Class Basket Options 296 19.1.2 Multi-asset Class Himalaya 297 19.2 Yield Enhancement 297 19.2.1 Rainbows 298 19.2.2 In- and Out-barriers 299 19.2.3 Multi-asset Class Digitals 299 19.2.4 Multi-asset Range Accruals 300 19.3 Multi-asset Class Views 301 19.4 Multi-asset Class Risk Hedging 303 20 Pricing Hybrid Derivatives 305 20.1 Additional Asset Class Models 305 20.1.1 Interest Rate Modelling 305 20.1.2 Commodity Modelling 309 20.1.3 FX Modelling 310 20.2 Copulas 312 20.2.1 Some Copula Theory 313 20.2.2 Modelling Dependencies in Copulas 314 20.2.3 Gaussian Copula 315 20.2.4 Pricing with Copulas 318 21 Dynamic Strategies and Thematic Indices 321 21.1 Portfolio Management Concepts 321 21.1.1 Mean–variance Analysis 321 21.1.2 Minimum-variance Frontier and Efficient Portfolios 322 21.1.3 Capital Asset Pricing Model 326 21.1.4 Sharpe Ratio 327 21.1.5 Portfolio Rebalancing 328 21.2 Dynamic Strategies 329 21.2.1 Why Dynamic Strategies? 329 21.2.2 Choosing the Assets 330 21.2.3 Building the Dynamic Strategy 330 21.3 Thematic Products 332 21.3.1 Demand for Thematic Products 333 21.3.2 Structuring a Thematic Index 334 21.3.3 Structured Products on Thematic Indices 335 21.3.4 Pricing Options on Thematic Indices 335 Appendices 339 A Models 341 A.1 Black–Scholes 341 A.1.1 Black–Scholes SDE 341 A.1.2 Black–Scholes PDE 341 A.2 Local Volatility Models 342 A.3 Stochastic Volatility 343 A.3.1 Heston’s Model 343 A.3.2 The SABR Model 345 A.4 Jump Models 346 A.5 Hull–White Interest Rate Model and Extensions 346 B Approximations 349 B.1 Approximations for Vanilla Prices and Greeks 349 B.2 Basket Price Approximation 351 B.3 ICBC/CBC Inequality 351 B.4 Digitals: Vega and the Position of the Forward 352 Postscript 355 Bibliography 357 Index 361

About the Author :
MOHAMED BOUZOUBAA is an experienced practitioner in the world of derivatives, and is currently Head of Derivatives Trading and Structuring at CDG Capital. His professional expertise spans the spectrum of topics in exotic options and hybrids having held positions in Equity Derivatives Sales at Société Générale in Paris, as a Risk and Fund Management expert at Sophis specializing in the risks involved in equity, credit and fixed income derivatives, and as a derivatives structurer at Bear Stearns/JP Morgan Chase in London and Equity Structured Products Manager at First Gulf Bank in Dubai. Mohamed holds masters degrees in Financial Engineering and in Applied Mathematics. ADEL OSSEIRAN is a mathematician by training. His work as a financial practitioner in derivative pricing includes working in front office roles as a quantitative analyst and as a derivatives structurer in London. He studied Mathematics at the University of Oxford and to PhD level in Financial Mathematics at Imperial College London.