The Handbook of Hybrid Securities: Convertible Bonds, CoCo Bonds, and Bail-In(The Wiley Finance Series)

Introducing a revolutionary new quantitative approach to hybrid securities valuation and risk management To an equity trader they are shares. For the trader at the fixed income desk, they are bonds (after all, they pay coupons, so what's the problem?). They are hybrid securities. Neither equity nor debt, they possess characteristics of both, and carry unique risks that cannot be ignored, but are often woefully misunderstood. The first and only book of its kind, The Handbook of Hybrid Securities dispels the many myths and misconceptions about hybrid securities and arms you with a quantitative, practical approach to dealing with them from a valuation and risk management point of view. Describes a unique, quantitative approach to hybrid valuation and risk management that uses new structural and multi-factor models Provides strategies for the full range of hybrid asset classes, including convertible bonds, preferreds, trust preferreds, contingent convertibles, bonds labeled "additional Tier 1," and more Offers an expert review of current regulatory climate regarding hybrids, globally, and explores likely political developments and their potential impact on the hybrid market The most up-to-date, in-depth book on the subject, this is a valuable working resource for traders, analysts and risk managers, and a indispensable reference for regulators

Table of Contents:
Reading this Book xv Acknowledgments xvii 1 Hybrid Assets 1 1.1 Introduction 1 1.2 Hybrid Capital 1 1.3 Preferreds 3 1.4 Convertible Bonds 5 1.5 Contingent Convertibles 7 1.6 Other Types of Hybrid Debt 7 1.6.1 Hybrid Bank Capital 7 1.6.2 Hybrid Corporate Capital 13 1.6.3 Toggle Bonds 14 1.7 Regulation 15 1.7.1 Making Failures Less Likely 15 1.7.2 Making Failures Less Disruptive 15 1.8 Bail-In Capital 16 1.9 Risk and Rating 17 1.9.1 Risk 17 1.9.2 Rating 18 1.10 Conclusion 18 2 Convertible Bonds 19 2.1 Introduction 19 2.2 Anatomy of a Convertible Bond 22 2.2.1 Final Payoff 22 2.2.2 Price Graph 22 2.2.3 Quotation of a Convertible Bond 23 2.2.4 Bond Floor (B F) 25 2.2.5 Parity 27 2.2.6 Convexity 27 2.2.7 Optional Conversion 33 2.2.8 Forced Conversion 35 2.2.9 Mandatory Conversion 35 2.3 Convertible Bond Arbitrage 37 2.3.1 Components of Risk 37 2.3.2 Delta 42 2.3.3 Delta Hedging 45 2.3.4 Different Notions of Delta 45 2.3.5 Greeks 46 2.4 Standard Features 47 2.4.1 Issuer Call 47 2.4.2 Put 50 2.4.3 Coupons 53 2.4.4 Dividends 56 2.5 Additional Features 58 2.5.1 Dividend Protection 58 2.5.2 Take-Over Protection 59 2.5.3 Refixes 60 2.6 Other Convertible Bond Types 62 2.6.1 Exchangeables 62 2.6.2 Synthetic Convertibles 63 2.6.3 Cross-Currency Convertibles 64 2.6.4 Reverse Convertibles 66 2.6.5 Convertible Preferreds 67 2.6.6 Make-Whole 67 2.6.7 Contingent Conversion 67 2.6.8 Convertible Bond Option 68 2.7 Convertible Bond Terminology 68 2.7.1 144a 68 2.7.2 Fixed-Income Metrics 68 2.8 Convertible Bond Market 73 2.8.1 Market Participants 73 2.8.2 Investors 74 2.9 Conclusion 76 3 Contingent Convertibles (CoCos) 77 3.1 Introduction 77 3.2 Definition 78 3.3 Anatomy 79 3.3.1 Loss-Absorption Mechanism 79 3.3.2 Trigger 83 3.3.3 Host Instrument 86 3.4 CoCos and Convertible Bonds 87 3.4.1 Forced vs. Optional Conversion 87 3.4.2 Negative vs. Positive Convexity 88 3.4.3 Limited vs. Unlimited Upside 89 3.4.4 Similarity to Reverse Convertibles 89 3.5 CoCos and Regulations 89 3.5.1 Introduction 89 3.5.2 Basel Framework 90 3.5.3 Basel I 91 3.5.4 Basel II 92 3.5.5 Basel III 93 3.5.6 Cocos in Basel III 101 3.5.7 High and Low-Trigger CoCos 104 3.6 Ranking in the Balance Sheet 106 3.7 Alternative Structures 106 3.8 Contingent Capital: Pro and Contra 107 3.8.1 Advantages 107 3.8.2 Disadvantages 107 3.8.3 Conclusion 110 4 Corporate Hybrids 113 4.1 Introduction 113 4.2 Issuer of Hybrid Debt 113 4.3 Investing in Hybrid Debt 114 4.4 Structure of a Corporate Hybrid Bond 115 4.4.1 Coupons 115 4.4.2 Replacement Capital Covenant 118 4.4.3 Issuer Calls 119 4.5 View of Rating Agencies 121 4.6 Risk in Hybrid Bonds 122 4.6.1 Subordination Risk 122 4.6.2 Deferral Risk 122 4.6.3 Extension Risk 122 4.7 Convexity in Hybrid Bonds 122 4.7.1 Case Study: Henkel 5.375% 2104 122 4.7.2 Duration Dynamics 126 4.8 Equity Character of Hybrid Bonds 126 5 Bail-In Bonds 127 5.1 Introduction 127 5.2 Definition 128 5.3 Resolution Regime 129 5.3.1 Resolution Tools 130 5.3.2 Timetable 130 5.4 Case Studies 133 5.4.1 Bail-In of Senior Bonds 133 5.4.2 Saving Lehman Brothers 134 5.5 Consequences of Bail-In 136 5.5.1 Higher Funding Costs 136 5.5.2 Higher GDP 136 5.5.3 Availability of Bail-In Bonds 136 5.5.4 Paying Bankers in Bail-In Bonds 136 5.6 Conclusion 137 6 Modeling Hybrids: An Introduction 139 6.1 Introduction 139 6.2 Heuristic Approaches 140 6.2.1 Corporate Hybrids: Yield of a Callable Bond 140 6.2.2 Convertible Bonds: Break Even 142 6.3 Building Models 143 6.3.1 Introduction 143 6.3.2 Martingales 145 6.3.3 Model Map 146 6.3.4 Cheapness 147 6.4 How Many Factors? 149 6.5 Sensitivity Analysis 152 6.5.1 Introduction 152 6.5.2 Non-linear Model 153 7 Modeling Hybrids: Stochastic Processes 159 7.1 Introduction 159 7.2 Probability Density Functions 159 7.2.1 Introduction 159 7.2.2 Normal Distribution 160 7.2.3 Lognormal Distribution 161 7.2.4 Exponential Distribution 162 7.2.5 Poisson Distribution 163 7.3 Brownian Motion 164 7.4 Ito Process 165 7.4.1 Introduction 165 7.4.2 Ito’s Lemma 166 7.4.3 Share Prices as Geometric Brownian Motion 169 7.5 Poisson Process 172 7.5.1 Definition 172 7.5.2 Advanced Poisson Processes 174 7.5.3 Conclusion 176 8 Modeling Hybrids: Risk Neutrality 177 8.1 Introduction 177 8.2 Closed-Form Solution 180 8.2.1 Introduction 180 8.2.2 Black–Scholes Solution 182 8.2.3 Solving the Black–Scholes Equation 183 8.2.4 Case Study: Reverse Convertible 184 8.3 Tree-Based Methods 186 8.3.1 Introduction 186 8.3.2 Framework 187 8.3.3 Geometry of the Trinomial Tree 189 8.3.4 Modeling Share Prices on a Trinomial Tree 193 8.3.5 European Options on a Trinomial Tree 199 8.3.6 American Options 200 8.3.7 Bermudan Options: Imposing a Particular Time Slice 203 8.4 Finite Difference Technique 204 8.5 Monte Carlo 205 8.5.1 Introduction 205 8.5.2 Generating Random Numbers 206 9 Modeling Hybrids: Advanced Issues 211 9.1 Tail Risk in Hybrids 211 9.2 Jump Diffusion 212 9.2.1 Introduction 212 9.2.2 Share Price Process with Jump to Default 214 9.2.3 Trinomial Trees with Jump to Default 217 9.2.4 Pricing Convertible Bonds with Jump Diffusion 221 9.2.5 Lost in Translation 226 9.3 Correlation 227 9.3.1 Correlation Risk in Hybrids 227 9.3.2 Definition 228 9.3.3 Correlating Wiener Processes 229 9.3.4 Cholesky Factorization 230 9.3.5 Cholesky Example 233 9.3.6 Correlating Events 234 9.3.7 Using Equity Correlation 235 9.3.8 Case Study: Correlated Defaults 237 9.3.9 Case Study: Asset Correlation vs. Default Correlation 238 9.4 Structural Models 240 9.5 Conclusion 242 10 Modeling Hybrids: Handling Credit 243 10.1 Credit Spread 243 10.1.1 Definition 243 10.1.2 Working with Credit Spreads 244 10.1.3 Option-Adjusted Spread 246 10.2 Default Intensity 246 10.2.1 Introduction 246 10.3 Credit Default Swaps 248 10.3.1 Definition 248 10.3.2 Example of a CDS Curve 250 10.3.3 Availability of CDS Data 250 10.3.4 Premium and Credit Leg 251 10.3.5 Valuation 252 10.3.6 Rule of Thumb 255 10.3.7 Market Convention 256 10.3.8 Case Study: Implied Default Probability 257 10.4 Credit Triangle 259 10.4.1 Definition 259 10.4.2 Case Study 260 10.4.3 The Big Picture 263 10.5 Stochastic Credit 263 11 Constant Elasticity of Variance 267 11.1 From Black–Scholes to CEV 267 11.1.1 Introduction 267 11.1.2 Leverage Effect 268 11.1.3 Link with Black–Scholes 269 11.2 Historical Parameter Estimation 270 11.3 Valuation: Analytical Solution 274 11.3.1 Moving Away from Black–Scholes 274 11.3.2 Semi-Closed-Form Formula 275 11.3.3 Numerical Example 276 11.4 Valuation: Trinomial Trees for CEV 277 11.4.1 American Options 277 11.4.2 Trinomial Trees for CEV 277 11.4.3 Numerical Example 279 11.5 Jump-Extended CEV Process 283 11.5.1 Introduction 283 11.5.2 JDCEV-Generated Skew 284 11.5.3 Convertible Bonds Priced under JDCEV 284 11.6 Case Study: Pricing Mandatories with CEV 286 11.6.1 Mandatory Conversion 286 11.6.2 Numerical Example 287 11.7 Case Study: Pricing Convertibles with a Reset 288 11.7.1 Refixing the Conversion Price 288 11.7.2 Involvement of CEV 291 11.7.3 Numerical Example 292 11.8 Calibration of CEV 295 11.8.1 Introduction 295 11.8.2 Local or Global Calibration 296 11.8.3 Calibrating CEV: Step by Step 296 12 Pricing Contingent Debt 301 12.1 Introduction 301 12.2 Credit Derivatives Method 302 12.2.1 Introduction 302 12.2.2 Loss 302 12.2.3 Trigger Intensity (λ Trigger) 303 12.2.4 CoCo Spread Calculation Example 305 12.2.5 Case Study: Lloyds Contingent Convertibles 305 12.3 Equity Derivatives Method 307 12.3.1 Introduction 307 12.3.2 Step 1: Zero-Coupon CoCo 308 12.3.3 Step 2: Adding Coupons 309 12.3.4 Numerical Example 311 12.3.5 Case Study: Lloyds Contingent Convertibles 313 12.3.6 Case Study: Tier 1 and Tier 2 CoCos 316 12.4 Coupon Deferral 317 12.5 Using Lattice Models 321 12.6 Linking Credit to Equity 323 12.6.1 Introduction 323 12.6.2 Hedging Credit Through Equity 326 12.6.3 Credit Elasticity 326 12.7 CoCos with Upside: CoCoCo 329 12.7.1 Downside Balanced with Upside 329 12.7.2 Numerical Example 330 12.8 Adding Stochastic Credit 333 12.8.1 Two-Factor Model 333 12.8.2 Monte Carlo Method 335 12.8.3 Pricing CoCos in a Two-Factor Model 337 12.8.4 Case Study 338 12.9 Avoiding Death Spirals 339 12.10 Appendix: Pricing Contingent Debt on a Trinomial Tree 341 12.10.1 Generalized Procedure 341 12.10.2 Positioning Nodes on the Trigger 343 12.10.3 Solving the CoCo Price 345 13 Multi-Factor Models for Hybrids 347 13.1 Introduction 347 13.2 Early Exercise 348 13.3 American Monte Carlo 352 13.3.1 Longstaff and Schwartz (LS) Technique 352 13.3.2 Convergence 356 13.3.3 Example: Longstaff and Schwartz (LS) Step by Step 356 13.3.4 Adding Calls and Puts 362 13.4 Multi-Factor Models 364 13.4.1 Adding Stochastic Interest Rates 364 13.4.2 Equity–Interest Rate Correlation 365 13.4.3 Adapting Longstaff and Schwartz (LS) 366 13.4.4 Convertible Bond under Stochastic Interest Rates 367 13.4.5 Adding Investor Put 371 13.5 Conclusion 371 References 373 Index 381