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
MOHAMED BOUZOUBAA is an experienced practitioner in theworld of derivatives, and is currently Head of Derivatives Tradingand Structuring at CDG Capital. His professional expertise spansthe spectrum of topics in exotic options and hybrids having heldpositions in Equity Derivatives Sales at SocieteGenerale in Paris, as a Risk and Fund Management expertat Sophis specializing in the risks involved in equity, credit andfixed income derivatives, and as a derivatives structurer at BearStearns/JP Morgan Chase in London and Equity Structured ProductsManager at First Gulf Bank in Dubai. Mohamed holds masters degreesin Financial Engineering and in Applied Mathematics. ADEL OSSEIRAN is a mathematician by training. His work asa financial practitioner in derivative pricing includes working infront office roles as a quantitative analyst and as a derivativesstructurer in London. He studied Mathematics at the University ofOxford and to PhD level in Financial Mathematics at ImperialCollege London.
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