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The Handbook of Hybrid Securities: Convertible Bonds, CoCo Bonds and Bail-In

ISBN: 978-1-118-44999-8
408 pages
May 2014
The Handbook of Hybrid Securities: Convertible Bonds, CoCo Bonds and Bail-In (1118449991) cover image

Description

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
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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 ( ) 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 (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

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Author Information

Jan De Spiegeleer (Geneva, Switzerland) is head of risk management at Jabre Capital Partners, a Geneva-based hedge fund. He earned an extensive knowledge of derivatives pricing, hedging and trading while working for KBC Financial Products in London, where he was managing director of the equity derivatives desk. He also ran his own market neutral statistical arbitrage hedge fund (EQM Europe) after founding Erasmus capital in 2004. Prior to this financial career, Jan served ten years in the Belgian Army as an Officer. With Wim Schoutens he co-authored the Handbook of Convertible Bonds published by Wiley.

Cynthia Van Hulle (Leuven, Belgium) is a full professor of Finance at the Department of Accounting, Finance and Insurance of the Faculty of Economics and Business at the Catholic University of Leuven. Over the last 20 years she has acquired extensive practical experience through her board memberships in the financial sector and organization of in-company training programs. She has published considerably in scientific journals a.o. Journal of Banking and Finance, Journal of Finance, Journal of Corporate Finance, European Financial Management, Journal of Business Research, Journal of Business, Finance and Accounting, Small Business Economics. She also held the Francqui-chair and is co-author of several books in corporate finance.

Wim Schoutens (Leuven, Belgium) is a research professor in financial engineering at the Department of Mathematics at the Catholic University of Leuven, Belgium. He has extensive practical experience of model implementation and is well known for his consulting work to the banking industry and other institutions. In particular, he is an independent expert advisor to the European Commission (DG-COMP) on impaired assets and asset relief measures and has assessed in that position more than EUR 1 trillion of assets; in particular he was one of the main expert advisors for the stress test on the Spanish banks and the related bailouts. Wim is also the author of several books including Contingent Convertibles (CoCos): Structure and Pricing, the first book ever on Contingent Capital and CoCo bonds (written together with Jan De Spiegeleer). He is Managing Editor of the International Journal of Theoretical and Applied Finance and Associate Editor of Mathematical Finance, Quantitative Finance and Review of Derivatives Research. Finally, he is member of the Belgium CPI commission and independent director of the Board of Assénagon Asset Management S.A.

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Reviews

“The Handbook of Hybrid Debt Securities is a modern state-of-the-art textbook in the field of hybrid debt instruments. It succeeds in combining a comprehensive introduction to the basic concepts of such securities with sophisticated modeling and valuation techniques.” (Financial Markets and Portfolio Management, February 2016)

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