FINANCIAL DERIVATIVE. INVESTMENTS An Introduction to Structured Products. Richard D. Bateson. Imperial College Press. University College London, UK

Transcription

1 FINANCIAL DERIVATIVE INVESTMENTS An Introduction to Structured Products Richard D. Bateson University College London, UK Imperial College Press

2 Contents Preface Guide to Acronyms Glossary of Notations v xv xvii Chapter 1: Introduction Introduction The Case for Derivative Investments Investment Criteria Types of Investors Families of Structured Products Structured equity products Structured interest rate products Structured credit products Other types of structured investment products Evolution of Derivatives Technology Equity derivative technology Interest rate derivative technology Credit derivative technology Introduction to Structuring Investment Products Issuing Structured Notes Financial or corporate issuers Special purpose vehicles (SPVs) Structured Product Fees 18 Chapter 2: Introduction to Swap Finance Introduction Zero Rates and Discount Factors Forward Rates Present Valuing Cash-Hows and Bonds Floating Rate Instruments 26

3 viii Financial Derivative Investments 2.6 Interest Rate Swaps Funding Legs for Structured Swaps Forwards and Futures Forward contracts Futures contracts Building Zero Curves 32 Chapter 3: Pricing Equity Options Call and Put Options Modelling Stock Prices The Black-Scholes Equation The Black-Scholes Option Pricing Equation Market Implied Volatility Option Price Sensitivities - "The Greeks" Delta Gamma Vega Theta Hedging portfolios using greeks Numerical Methods Binomial trees Monte Carlo simulation Digitals and Barrier Options FX Options and Quantos 58 Chapter 4: Equity Structured Products Introduction Reverse Convertibles Structuring reverse convertibles Discount reverse convertibles Knock-in reverse convertibles Lock-up reverse convertibles Leveraged reverse convertibles Auto-callables and extendibles Contingent coupon reverse convertibles Reverse convertible summary Protected Bull Notes Average protected bull notes Capped protected bull notes Protected Cliquet Notes Reverse cliquets Scaled cliquet protected notes 87

4 Contents ix 4.5 Multi-Barrier Protected Notes Leveraged Bull Notes Summary of Equity Structured Products 92 Chapter 5: Basket Equity Products Introduction Basket Notes Protected Basket Bull Notes Average protected basket bull notes Capped protected basket bull notes Protected Basket Cliquet Notes Basket Reverse Convertibles Protected Multiple Binary Notes Rainbow Notes Protected rainbow notes Worst-of Protected Notes Everest protected notes Power reverse convertibles Performance Select Protected Notes Atlas protected notes Himalaya protected notes Worst-of Knock-out Notes Pulsar protected notes Altiplano and Neptune protected notes Summary 127 Chapter 6: Pricing Interest Rate Products Introduction Approaches to Modelling Interest Rates Black's Model Black's model for forward rates Black's cap Market Volatility of Caps and Floors The Hull-White Model The Hull-White caplet Swaptions Black's Model for Swap Rates Black's model for European swaptions Hull-White Swaptions Hull-White Model Calibration Numerical Methods Hull-White model trinomial trees 145

5 x Financial Derivative Investments Hull-White Monte Carlo Other Interest Rate Models Hedging an Interest Rate Derivatives Book 149 Chapter 7: Interest Rate Products Introduction Capped/Floored Notes Capped floating rate note Reverse floating rate note Barrier Notes Digital barrier note Minimum payoff range note Accrual Notes Digital accrual note Barrier accrual floating rate note Minimum payoff range accrual notes Chooser Notes Range Reset Notes Ratchet Notes Callable Notes Constant Maturity Notes Yield Curve Notes FX Linked Notes 170 Chapter 8: Pricing Credit Derivatives Introduction Market Credit Curves Capital Structure and Leverage What Happens in a Bankruptcy? Credit Ratings and Rating Agencies Rating agencies Historical default probabilities Recovery rates Asset Swaps Credit Default Swaps (CDS) Basis Packages Credit Pricing Models Stochastic firm value models Reduced form models Pricing Credit Default Swaps Building Hazard Rate Curves I.I Recovery rates in credit curve building 198

6 Contents xi 8.12 Modelling "Risky" Bonds Digital CDS Loan Credit Default Swaps (LCDS) Counterparty Default Correlation Modelling and Trading Default Correlation 201 Chapter 9: Structured Credit Products Introduction Credit Linked Notes Floating rate credit linked note Fixed rate credit linked note SPV issued credit linked note Leveraged credit linked note Basket Credit Linked Note Principal Protected Credit Linked Note Basket principal protected note First-to-Default Notes Principal protected first-to-default notes Collateralised Debt Obligations CashCDOs Synthetic CDOs CDOs of ABS and "CDO-squared" Pricing synthetic CDOs The rationale for investing in CDOs 233 Chapter 10: Fund Options and Hybrids Introduction Fund Linked Notes CPPI Investments Hybrid Products 242 Appendix A: Introduction to Swap Finance 247 A.I Discount Factors, Zero Rates and Forward Rates 247 A.2 Day Count Conventions 248 A.3 Other Types of Interest Rate Swap 249 A.4 Convexity in Futures and Floating Rate Contracts 249 A.5 Analytical Convexity Adjustments 251 A.6 Pricing LIBOR-in-Arrears Swaps 252 A.7 Pricing a CMS Swap 252 A.8 Pricing a Diff or Quanto Swap 253

7 xii Financial Derivative Investments Appendix B: Pricing Equity Options 255 B. 1 Modelling Stock Prices 255 B.2 Ito's Lemma 256 B.3 The Black-Scholes Equation 258 B.4 Some Important Black-Scholes Results 259 B.5 The Black-Scholes Option Pricing Equation 261 B.6 Black-Scholes with Continuous Dividends 263 B.7 Moment Generating Function and Girsanov's Theorem 264 B.8 The "Greeks" 265 B.8.1 Delta 266 B.8.2 Gamma 266 B.8.3 Vega 267 B.8.4Theta 267 B.8.5Rho 267 B.9 Binomial Trees 268 B.10 Pricing Convertible Bonds on a Binomial Tree 271 B.I 1 Three-Dimensional Binomial Trees 272 B.I2 Monte Carlo Simulation 273 B.I2.1 Monte Carlo simulation of maximum lookback call options 274 B Monte Carlo simulation of average rate call options 275 B.13 Finite Difference Methods 275 B.14 Alternatives to the Black-Scholes Model 277 B.14.1 The CEV model 277 B The Merton model 277 B.15 Implied Volatility Model 278 B.I6 Stochastic Equity Volatility Models 279 B.16.1 The Heston model 279 B.16.2 The SABR model 280 B.17 Effects of Transaction Costs and Discrete Hedging 281 B. 18 Effect of Realised Volatility and Variance Swaps 282 B.19 Pricing FX Options Using Black-Scholes 283 B.20 Quanto Corrections 284 Appendix C: Equity Structured Products 287 C.I Reverse Convertibles 287 C.2 Discount Reverse Convertibles 287 C.3 Knock-in Reverse Convertibles 288 C.4 Lock-up Reverse Convertibles 288 C.5 Digital Options 288 C.6 Barrier Options 289 C.7 Leveraged Reverse Convertibles 290 C.8 Protected Bull Notes 291

8 Contents xiii C.9 Average Protected Bull Notes 291 CIO Pricing Average Rate Options 291 C.ll Capped Protected Bull Notes 293 C.12 Protected Cliquet Notes 293 C.13 Forward Start and Cliquet Options 294 C. 14 Multi-Barrier Protected Notes 294 Appendix D: Equity Basket Products 295 D.I Equity Correlation 295 D.2 Protected Basket Notes 295 D.3 Basket Pricing Using a Single Factor Approximation 296 D.4 Basket Monte Carlo Pricing 297 D.5 Average Protected Basket Bull Notes 298 D.6 Protected Basket Cliquet Notes 298 D.7 Protected Multiple Binary Notes 298 D.8 Rainbow Notes 299 D.9 Worst-of Protected Notes 300 D.10 Best-of and Worst-of Closed Form on Two Assets 300 D.I 1 Everest Protected Notes 301 D. 12 Power Reverse Convertibles 301 D.I3 Pulsar Protected Notes 302 D.14 Altiplano and Neptune Protected Notes 302 Appendix E: Pricing Interest Rate Products 303 E.I Different Types of Interest Rate Models 303 E.2 Black's Model for Forward Rates 303 E.3 Black's Cap 305 E.4 The Hull-White Model 306 E.5 The Hull-White Caplet 308 E.6 Black's Model for European Swaptions 310 E.7 Hull-White Swaptions 31 1 E.8 Hull-White Model Trinomial Trees 312 E.9 The Heath, Jarrow and Morton Model 317 E. 10 The LIBOR Market Model 319 Appendix F: Interest Rate Products 323 F.I Capped/Floored Notes 323 F.2 Reverse Floating Rate Note 324 F.3 Digital Barrier Note 324 F.4 Minimum Payoff Range Note 325 F.5 Digital Caps and Floors 325 F.6 Digital Accrual Note 326

9 xiv Financial Derivative Investments F.7 Barrier Accrual Floating Rate Note 327 F.8 Minimum Payoff Range Accrual Notes 327 F.9 Chooser Notes 328 Appendix G: Pricing Credit Derivatives 329 G.I Par Asset Swap 329 G.2 Market Value Asset Swap 330 G.3Z-Spread 330 G.4 Stochastic Firm Value Models 330 G.4.1 Simple maturity default model 330 G.4.2 CreditGrades model 332 G.5 The Reduced Form Model and Poisson Default Processes 333 G.6 Pricing Credit Default Swaps (CDS) 334 G.7 Building a Simple Hazard Rate Curve 335 G.8 Modelling "Risky" Bonds 336 G.9 Digital CDS 337 G.10 Correlated Credit Default Swap 338 G. 11 Normal Copula Model for Correlated Default Times 338 G. 12 Synthetic CDO Valuation G.13 Extending the Normal Copula Approach 341 Appendix H: Structured Credit Products 343 H. I Fixed Rate Credit Linked Note 343 H.2 Basket Credit Linked Note 343 H.3 Principal Protected Credit Linked Note 344 H.4 Basket Principal Protected Note 344 H.5 First-to-Default Notes 344 Appendix I: Fund Options and Hybrids CPPI Methodology Pricing Hybrids 346 Further Reading 347 Index 351