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.

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• List of Symbols and Abbreviations xviiPreface xixPart I Foundations 11 Basic Instruments 31.1 Introduction 31.2 Interest Rates 31.2.1 LIBOR vs Treasury Rates 41.2.2 Yield Curves 41.2.3 Time Value of Money 51.2.4 Bonds 61.2.5 Zero Coupon Bonds 71.3 Equities and Currencies 81.3.1 Stocks 81.3.2 Foreign Exchange 101.3.3 Indices 101.3.4 Exchange-traded Funds 111.3.5 Forward Contracts 111.3.6 Futures 121.4 Swaps 131.4.1 Interest Rate Swaps 131.4.2 Cross-currency Swaps 141.4.3 Total Return Swaps 161.4.4 Asset Swaps 161.4.5 Dividend Swaps 162 The World of Structured Products 192.1 The Products 192.1.1 The Birth of Structured Products 192.1.2 Structured Product Wrappers 202.1.3 The Structured Note 202.2 The Sell Side 212.2.1 Sales and Marketing 212.2.2 Traders and Structurers 222.3 The Buy Side 232.3.1 Retail Investors 232.3.2 Institutional Investors 242.3.3 Bullish vs Bearish, the Economic Cycle 242.3.4 Credit Risk and Collateralized Lines 252.4 The Market 262.4.1 Issuing a Structured Product 262.4.2 Liquidity and a Two-way Market 272.5 Example of an Equity Linked Note 283 Vanilla Options 313.1 General Features of Options 313.2 Call and Put Option Payoffs 323.3 Put–call Parity and Synthetic Options 343.4 Black–Scholes Model Assumptions 353.4.1 Risk-neutral Pricing 363.5 Pricing a European Call Option 373.6 Pricing a European Put Option 383.7 The Cost of Hedging 403.8 American Options 423.9 Asian Options 433.10 An Example of the Structuring Process 443.10.1 Capital Protection and Equity Participation 443.10.2 Capital at Risk and Higher Participation 464 Volatility, Skew and Term Structure 494.1 Volatility 494.1.1 Realized Volatility 494.1.2 Implied Volatility 514.2 The Volatility Surface 524.2.1 The Implied Volatility Skew 524.2.2 Term Structure of Volatilities 564.3 Volatility Models 574.3.1 Model Choice and Model Risk 574.3.2 Black–Scholes or Flat Volatility 584.3.3 Local Volatility 604.3.4 Stochastic Volatility 625 Option Sensitivities: Greeks 655.1 Delta 665.2 Gamma 725.3 Vega 745.4 Theta 765.5 Rho 775.6 Relationships between the Greeks 785.7 Volga and Vanna 805.7.1 Vega–Gamma (Volga) 805.7.2 Vanna 815.8 Multi-asset Sensitivities 815.9 Approximations to Black–Scholes and Greeks 826 Strategies Involving Options 876.1 Traditional Hedging Strategies 876.1.1 Protective Puts 876.1.2 Covered Calls 896.2 Vertical Spreads 906.2.1 Bull Spreads 906.2.2 Bear Spreads 936.3 Other Spreads 966.3.1 Butterfly Spreads 966.3.2 Condor Spreads 986.3.3 Ratio Spreads 996.3.4 Calendar Spreads 996.4 Option Combinations 1006.4.1 Straddles 1006.4.2 Strangles 1016.5 Arbitrage Freedom of the Implied Volatility Surface 1027 Correlation 1057.1 Multi-asset Options 1057.2 Correlation: Measurements and Interpretation 1067.2.1 Realized Correlation 1067.2.2 Correlation Matrices 1097.2.3 Portfolio Variance 1107.2.4 Implied Correlation 1117.2.5 Correlation Skew 1137.3 Basket Options 1147.4 Quantity Adjusting Options: “Quantos” 1167.4.1 Quanto Payoffs 1167.4.2 Quanto Correlation and Quanto Option Pricing 1167.4.3 Hedging Quanto Risk 1177.5 Trading Correlation 1187.5.1 Straddles: Index versus Constituents 1187.5.2 Correlation Swaps 118Part II Exotic Derivatives and Structured Products 1218 Dispersion 1238.1 Measures of Dispersion and Interpretations 1238.2 Worst-of Options 1258.2.1 Worst-of Call 1258.2.2 Worst-of Put 1278.2.3 Market Trends in Worst-of Options 1288.3 Best-of options 1298.3.1 Best-of Call 1298.3.2 Best-of Put 1318.3.3 Market Trends in Best-of Options 1329 Dispersion Options 1359.1 Rainbow Options 1359.1.1 Payoff Mechanism 1359.1.2 Risk Analysis 1369.2 Individually Capped Basket Call (ICBC) 1379.2.1 Payoff Mechanism 1379.2.2 Risk Analysis 1389.3 Outperformance Options 1419.3.1 Payoff Mechanism 1419.3.2 Risk Analysis 1429.4 Volatility Models 14310 Barrier Options 14510.1 Barrier Option Payoffs 14510.1.1 Knock-out Options 14510.1.2 Knock-in Options 14810.1.3 Summary 15010.2 Black–Scholes Valuation 15110.2.1 Parity Relationships 15110.2.2 Closed Formulas for Continuously Monitored Barriers 15110.2.3 Adjusting for Discrete Barriers 15410.3 Hedging Down-and-in Puts 15510.3.1 Monitoring the Barrier 15510.3.2 Volatility and Down-and-in Puts 15710.3.3 Dispersion Effect on Worst-of Down-and-in Puts 15810.4 Barriers in Structured Products 16010.4.1 Multi-asset Shark 16010.4.2 Single Asset Reverse Convertible 16310.4.3 Worst-of Reverse Convertible 16411 Digitals 16711.1 European Digitals 16711.1.1 Digital Payoffs and Pricing 16711.1.2 Replicating a European Digital 16911.1.3 Hedging a Digital 16911.2 American Digitals 17211.3 Risk Analysis 17411.3.1 Single Asset Digitals 17411.3.2 Digital Options with Dispersion 17611.3.3 Volatility Models for Digitals 17711.4 Structured Products Involving European Digitals 17811.4.1 Strip of Digitals Note 17811.4.2 Growth and Income 17911.4.3 Bonus Steps Certificate 18111.5 Structured Products Involving American Digitals 18311.5.1 Wedding Cake 18311.5.2 Range Accrual 18411.6 Outperformance Digital 18511.6.1 Payoff Mechanism 18511.6.2 Correlation Skew and Other Risks 18612 Autocallable Structures 18712.1 Single Asset Autocallables 18712.1.1 General Features 18712.1.2 Interest Rate/Equity Correlation 19012.2 Autocallable Participating Note 19212.3 Autocallables with Down-and-in Puts 19412.3.1 Adding the Put Feature 19412.3.2 Twin-Wins 19412.3.3 Autocallables with Bonus Coupons 19612.4 Multi-asset Autocallables 19812.4.1 Worst-of Autocallables 19812.4.2 Snowball Effect and Worst-of put Feature 20012.4.3 Outperformance Autocallables 202Part III More on Exotic Structures 20513 The Cliquet Family 20713.1 Forward Starting Options 20713.2 Cliquets with Local Floors and Caps 20813.2.1 Payoff Mechanism 20913.2.2 Forward Skew and Other Risks 21013.3 Cliquets with Global Floors and Caps 21013.3.1 Vega Convexity 21313.3.2 Levels of These Risks 21513.4 Reverse Cliquets 21714 More Cliquets and Related Structures 21914.1 Other Cliquets 21914.1.1 Digital Cliquets 21914.1.2 Bearish Cliquets 22014.1.3 Variable Cap Cliquets 22114.1.4 Accumulators/Lock-in Cliquets 22214.1.5 Replacement Cliquets 22214.2 Multi-asset Cliquets 22414.2.1 Multi-asset Cliquet Payoffs 22414.2.2 Multi-asset Cliquet Risks 22514.3 Napoleons 22614.3.1 The Napoleon Structure 22614.3.2 The Bearish Napoleon 22714.4 Lookback Options 22714.4.1 The Various Lookback Payoffs 22714.4.2 Hedging Lookbacks 22814.4.3 Sticky Strike and Sticky Delta 22914.4.4 Skew Risk in Lookbacks 22915 Mountain Range Options 23115.1 Altiplano 23115.2 Himalaya 23315.3 Everest 23515.4 Kilimanjaro Select 23615.5 Atlas 23815.6 Pricing Mountain Range Products 23916 Volatility Derivatives 24316.1 The Need for Volatility Derivatives 24316.2 Traditional Methods for Trading Volatility 24316.3 Variance Swaps 24416.3.1 Payoff Description 24516.3.2 Variance vs Volatility Swaps 24616.3.3 Replication and Pricing of Variance Swaps 24616.3.4 Capped Variance Swaps 24816.3.5 Forward Starting Variance Swaps 24916.3.6 Variance Swap Greeks 24916.4 Variations on Variance Swaps 25016.4.1 Corridor Variance Swaps 25016.4.2 Conditional Variance Swaps 25116.4.3 Gamma Swaps 25316.5 Options on Realized Variance 25416.6 The VIX: Volatility Indices 25416.6.1 Options on the VIX 25516.6.2 Combining Equity and Volatility Indices 25616.7 Variance Dispersion 256Part IV Hybrid Derivatives and Dynamic Strategies 25917 Asset Classes (I) 26117.1 Interest Rates 26217.1.1 Forward Rate Agreements 26217.1.2 Constant Maturity Swaps 26317.1.3 Bonds 26417.1.4 Yield Curves 26517.1.5 Zero Coupon, LIBOR and Swap Rates 26717.1.6 Interest Rate Swaptions 26817.1.7 Interest Rate Caps and Floors 26917.1.8 The SABR Model 27017.1.9 Exotic Interest Rate Structures 27117.2 Commodities 27217.2.1 Forward and Futures Curves, Contango and Backwardation 27317.2.2 Commodity Vanillas and Skew 27618 Asset Classes (II) 27918.1 Foreign Exchange 27918.1.1 Forward and Futures Curves 27918.1.2 FX Vanillas and Volatility Smiles 28118.1.3 FX Implied Correlations 28718.1.4 FX Exotics 28718.2 Inflation 28818.2.1 Inflation and the Need for Inflation Products 28918.2.2 Inflation Swaps 28918.2.3 Inflation Bonds 29018.2.4 Inflation Derivatives 29018.3 Credit 29118.3.1 Bonds and Default Risk 29218.3.2 Credit Default Swaps 29319 Structuring Hybrid Derivatives 29519.1 Diversification 29519.1.1 Multi-asset Class Basket Options 29619.1.2 Multi-asset Class Himalaya 29719.2 Yield Enhancement 29719.2.1 Rainbows 29819.2.2 In- and Out-barriers 29919.2.3 Multi-asset Class Digitals 29919.2.4 Multi-asset Range Accruals 30019.3 Multi-asset Class Views 30119.4 Multi-asset Class Risk Hedging 30320 Pricing Hybrid Derivatives 30520.1 Additional Asset Class Models 30520.1.1 Interest Rate Modelling 30520.1.2 Commodity Modelling 30920.1.3 FX Modelling 31020.2 Copulas 31220.2.1 Some Copula Theory 31320.2.2 Modelling Dependencies in Copulas 31420.2.3 Gaussian Copula 31520.2.4 Pricing with Copulas 31821 Dynamic Strategies and Thematic Indices 32121.1 Portfolio Management Concepts 32121.1.1 Mean–variance Analysis 32121.1.2 Minimum-variance Frontier and Efficient Portfolios 32221.1.3 Capital Asset Pricing Model 32621.1.4 Sharpe Ratio 32721.1.5 Portfolio Rebalancing 32821.2 Dynamic Strategies 32921.2.1 Why Dynamic Strategies? 32921.2.2 Choosing the Assets 33021.2.3 Building the Dynamic Strategy 33021.3 Thematic Products 33221.3.1 Demand for Thematic Products 33321.3.2 Structuring a Thematic Index 33421.3.3 Structured Products on Thematic Indices 33521.3.4 Pricing Options on Thematic Indices 335Appendices 339A Models 341A.1 Black–Scholes 341A.1.1 Black–Scholes SDE 341A.1.2 Black–Scholes PDE 341A.2 Local Volatility Models 342A.3 Stochastic Volatility 343A.3.1 Heston’s Model 343A.3.2 The SABR Model 345A.4 Jump Models 346A.5 Hull–White Interest Rate Model and Extensions 346B Approximations 349B.1 Approximations for Vanilla Prices and Greeks 349B.2 Basket Price Approximation 351B.3 ICBC/CBC Inequality 351B.4 Digitals: Vega and the Position of the Forward 352Postscript 355Bibliography 357Index 361

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.

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• List of Symbols and Abbreviations xviiPreface xixPart I Foundations 11 Basic Instruments 31.1 Introduction 31.2 Interest Rates 31.2.1 LIBOR vs Treasury Rates 41.2.2 Yield Curves 41.2.3 Time Value of Money 51.2.4 Bonds 61.2.5 Zero Coupon Bonds 71.3 Equities and Currencies 81.3.1 Stocks 81.3.2 Foreign Exchange 101.3.3 Indices 101.3.4 Exchange-traded Funds 111.3.5 Forward Contracts 111.3.6 Futures 121.4 Swaps 131.4.1 Interest Rate Swaps 131.4.2 Cross-currency Swaps 141.4.3 Total Return Swaps 161.4.4 Asset Swaps 161.4.5 Dividend Swaps 162 The World of Structured Products 192.1 The Products 192.1.1 The Birth of Structured Products 192.1.2 Structured Product Wrappers 202.1.3 The Structured Note 202.2 The Sell Side 212.2.1 Sales and Marketing 212.2.2 Traders and Structurers 222.3 The Buy Side 232.3.1 Retail Investors 232.3.2 Institutional Investors 242.3.3 Bullish vs Bearish, the Economic Cycle 242.3.4 Credit Risk and Collateralized Lines 252.4 The Market 262.4.1 Issuing a Structured Product 262.4.2 Liquidity and a Two-way Market 272.5 Example of an Equity Linked Note 283 Vanilla Options 313.1 General Features of Options 313.2 Call and Put Option Payoffs 323.3 Put–call Parity and Synthetic Options 343.4 Black–Scholes Model Assumptions 353.4.1 Risk-neutral Pricing 363.5 Pricing a European Call Option 373.6 Pricing a European Put Option 383.7 The Cost of Hedging 403.8 American Options 423.9 Asian Options 433.10 An Example of the Structuring Process 443.10.1 Capital Protection and Equity Participation 443.10.2 Capital at Risk and Higher Participation 464 Volatility, Skew and Term Structure 494.1 Volatility 494.1.1 Realized Volatility 494.1.2 Implied Volatility 514.2 The Volatility Surface 524.2.1 The Implied Volatility Skew 524.2.2 Term Structure of Volatilities 564.3 Volatility Models 574.3.1 Model Choice and Model Risk 574.3.2 Black–Scholes or Flat Volatility 584.3.3 Local Volatility 604.3.4 Stochastic Volatility 625 Option Sensitivities: Greeks 655.1 Delta 665.2 Gamma 725.3 Vega 745.4 Theta 765.5 Rho 775.6 Relationships between the Greeks 785.7 Volga and Vanna 805.7.1 Vega–Gamma (Volga) 805.7.2 Vanna 815.8 Multi-asset Sensitivities 815.9 Approximations to Black–Scholes and Greeks 826 Strategies Involving Options 876.1 Traditional Hedging Strategies 876.1.1 Protective Puts 876.1.2 Covered Calls 896.2 Vertical Spreads 906.2.1 Bull Spreads 906.2.2 Bear Spreads 936.3 Other Spreads 966.3.1 Butterfly Spreads 966.3.2 Condor Spreads 986.3.3 Ratio Spreads 996.3.4 Calendar Spreads 996.4 Option Combinations 1006.4.1 Straddles 1006.4.2 Strangles 1016.5 Arbitrage Freedom of the Implied Volatility Surface 1027 Correlation 1057.1 Multi-asset Options 1057.2 Correlation: Measurements and Interpretation 1067.2.1 Realized Correlation 1067.2.2 Correlation Matrices 1097.2.3 Portfolio Variance 1107.2.4 Implied Correlation 1117.2.5 Correlation Skew 1137.3 Basket Options 1147.4 Quantity Adjusting Options: “Quantos” 1167.4.1 Quanto Payoffs 1167.4.2 Quanto Correlation and Quanto Option Pricing 1167.4.3 Hedging Quanto Risk 1177.5 Trading Correlation 1187.5.1 Straddles: Index versus Constituents 1187.5.2 Correlation Swaps 118Part II Exotic Derivatives and Structured Products 1218 Dispersion 1238.1 Measures of Dispersion and Interpretations 1238.2 Worst-of Options 1258.2.1 Worst-of Call 1258.2.2 Worst-of Put 1278.2.3 Market Trends in Worst-of Options 1288.3 Best-of options 1298.3.1 Best-of Call 1298.3.2 Best-of Put 1318.3.3 Market Trends in Best-of Options 1329 Dispersion Options 1359.1 Rainbow Options 1359.1.1 Payoff Mechanism 1359.1.2 Risk Analysis 1369.2 Individually Capped Basket Call (ICBC) 1379.2.1 Payoff Mechanism 1379.2.2 Risk Analysis 1389.3 Outperformance Options 1419.3.1 Payoff Mechanism 1419.3.2 Risk Analysis 1429.4 Volatility Models 14310 Barrier Options 14510.1 Barrier Option Payoffs 14510.1.1 Knock-out Options 14510.1.2 Knock-in Options 14810.1.3 Summary 15010.2 Black–Scholes Valuation 15110.2.1 Parity Relationships 15110.2.2 Closed Formulas for Continuously Monitored Barriers 15110.2.3 Adjusting for Discrete Barriers 15410.3 Hedging Down-and-in Puts 15510.3.1 Monitoring the Barrier 15510.3.2 Volatility and Down-and-in Puts 15710.3.3 Dispersion Effect on Worst-of Down-and-in Puts 15810.4 Barriers in Structured Products 16010.4.1 Multi-asset Shark 16010.4.2 Single Asset Reverse Convertible 16310.4.3 Worst-of Reverse Convertible 16411 Digitals 16711.1 European Digitals 16711.1.1 Digital Payoffs and Pricing 16711.1.2 Replicating a European Digital 16911.1.3 Hedging a Digital 16911.2 American Digitals 17211.3 Risk Analysis 17411.3.1 Single Asset Digitals 17411.3.2 Digital Options with Dispersion 17611.3.3 Volatility Models for Digitals 17711.4 Structured Products Involving European Digitals 17811.4.1 Strip of Digitals Note 17811.4.2 Growth and Income 17911.4.3 Bonus Steps Certificate 18111.5 Structured Products Involving American Digitals 18311.5.1 Wedding Cake 18311.5.2 Range Accrual 18411.6 Outperformance Digital 18511.6.1 Payoff Mechanism 18511.6.2 Correlation Skew and Other Risks 18612 Autocallable Structures 18712.1 Single Asset Autocallables 18712.1.1 General Features 18712.1.2 Interest Rate/Equity Correlation 19012.2 Autocallable Participating Note 19212.3 Autocallables with Down-and-in Puts 19412.3.1 Adding the Put Feature 19412.3.2 Twin-Wins 19412.3.3 Autocallables with Bonus Coupons 19612.4 Multi-asset Autocallables 19812.4.1 Worst-of Autocallables 19812.4.2 Snowball Effect and Worst-of put Feature 20012.4.3 Outperformance Autocallables 202Part III More on Exotic Structures 20513 The Cliquet Family 20713.1 Forward Starting Options 20713.2 Cliquets with Local Floors and Caps 20813.2.1 Payoff Mechanism 20913.2.2 Forward Skew and Other Risks 21013.3 Cliquets with Global Floors and Caps 21013.3.1 Vega Convexity 21313.3.2 Levels of These Risks 21513.4 Reverse Cliquets 21714 More Cliquets and Related Structures 21914.1 Other Cliquets 21914.1.1 Digital Cliquets 21914.1.2 Bearish Cliquets 22014.1.3 Variable Cap Cliquets 22114.1.4 Accumulators/Lock-in Cliquets 22214.1.5 Replacement Cliquets 22214.2 Multi-asset Cliquets 22414.2.1 Multi-asset Cliquet Payoffs 22414.2.2 Multi-asset Cliquet Risks 22514.3 Napoleons 22614.3.1 The Napoleon Structure 22614.3.2 The Bearish Napoleon 22714.4 Lookback Options 22714.4.1 The Various Lookback Payoffs 22714.4.2 Hedging Lookbacks 22814.4.3 Sticky Strike and Sticky Delta 22914.4.4 Skew Risk in Lookbacks 22915 Mountain Range Options 23115.1 Altiplano 23115.2 Himalaya 23315.3 Everest 23515.4 Kilimanjaro Select 23615.5 Atlas 23815.6 Pricing Mountain Range Products 23916 Volatility Derivatives 24316.1 The Need for Volatility Derivatives 24316.2 Traditional Methods for Trading Volatility 24316.3 Variance Swaps 24416.3.1 Payoff Description 24516.3.2 Variance vs Volatility Swaps 24616.3.3 Replication and Pricing of Variance Swaps 24616.3.4 Capped Variance Swaps 24816.3.5 Forward Starting Variance Swaps 24916.3.6 Variance Swap Greeks 24916.4 Variations on Variance Swaps 25016.4.1 Corridor Variance Swaps 25016.4.2 Conditional Variance Swaps 25116.4.3 Gamma Swaps 25316.5 Options on Realized Variance 25416.6 The VIX: Volatility Indices 25416.6.1 Options on the VIX 25516.6.2 Combining Equity and Volatility Indices 25616.7 Variance Dispersion 256Part IV Hybrid Derivatives and Dynamic Strategies 25917 Asset Classes (I) 26117.1 Interest Rates 26217.1.1 Forward Rate Agreements 26217.1.2 Constant Maturity Swaps 26317.1.3 Bonds 26417.1.4 Yield Curves 26517.1.5 Zero Coupon, LIBOR and Swap Rates 26717.1.6 Interest Rate Swaptions 26817.1.7 Interest Rate Caps and Floors 26917.1.8 The SABR Model 27017.1.9 Exotic Interest Rate Structures 27117.2 Commodities 27217.2.1 Forward and Futures Curves, Contango and Backwardation 27317.2.2 Commodity Vanillas and Skew 27618 Asset Classes (II) 27918.1 Foreign Exchange 27918.1.1 Forward and Futures Curves 27918.1.2 FX Vanillas and Volatility Smiles 28118.1.3 FX Implied Correlations 28718.1.4 FX Exotics 28718.2 Inflation 28818.2.1 Inflation and the Need for Inflation Products 28918.2.2 Inflation Swaps 28918.2.3 Inflation Bonds 29018.2.4 Inflation Derivatives 29018.3 Credit 29118.3.1 Bonds and Default Risk 29218.3.2 Credit Default Swaps 29319 Structuring Hybrid Derivatives 29519.1 Diversification 29519.1.1 Multi-asset Class Basket Options 29619.1.2 Multi-asset Class Himalaya 29719.2 Yield Enhancement 29719.2.1 Rainbows 29819.2.2 In- and Out-barriers 29919.2.3 Multi-asset Class Digitals 29919.2.4 Multi-asset Range Accruals 30019.3 Multi-asset Class Views 30119.4 Multi-asset Class Risk Hedging 30320 Pricing Hybrid Derivatives 30520.1 Additional Asset Class Models 30520.1.1 Interest Rate Modelling 30520.1.2 Commodity Modelling 30920.1.3 FX Modelling 31020.2 Copulas 31220.2.1 Some Copula Theory 31320.2.2 Modelling Dependencies in Copulas 31420.2.3 Gaussian Copula 31520.2.4 Pricing with Copulas 31821 Dynamic Strategies and Thematic Indices 32121.1 Portfolio Management Concepts 32121.1.1 Mean–variance Analysis 32121.1.2 Minimum-variance Frontier and Efficient Portfolios 32221.1.3 Capital Asset Pricing Model 32621.1.4 Sharpe Ratio 32721.1.5 Portfolio Rebalancing 32821.2 Dynamic Strategies 32921.2.1 Why Dynamic Strategies? 32921.2.2 Choosing the Assets 33021.2.3 Building the Dynamic Strategy 33021.3 Thematic Products 33221.3.1 Demand for Thematic Products 33321.3.2 Structuring a Thematic Index 33421.3.3 Structured Products on Thematic Indices 33521.3.4 Pricing Options on Thematic Indices 335Appendices 339A Models 341A.1 Black–Scholes 341A.1.1 Black–Scholes SDE 341A.1.2 Black–Scholes PDE 341A.2 Local Volatility Models 342A.3 Stochastic Volatility 343A.3.1 Heston’s Model 343A.3.2 The SABR Model 345A.4 Jump Models 346A.5 Hull–White Interest Rate Model and Extensions 346B Approximations 349B.1 Approximations for Vanilla Prices and Greeks 349B.2 Basket Price Approximation 351B.3 ICBC/CBC Inequality 351B.4 Digitals: Vega and the Position of the Forward 352Postscript 355Bibliography 357Index 361