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

Hybrid financial securities contain properties of both debt and equity.  Blending the properties of two easy–to–understand asset classes such as equity and bonds into a hybrid does not leave us an instrument with straightforward properties and therefore hybrids are often misunderstood and miss–sold. The high yields offered by these securities attract investors, this yield is a compensation for the particular complex anatomy of these instruments. This complexity results from the introduction of several coupon deferral mechanisms and issuer calls with or without set–up features. The newest member in this asset class is a CoCo bond, where the investor is possibly exposed to a particular loss absorption mechanism. Through practical examples and case studies, The Handbook of Hybrid Securities: Convertible Bonds, CoCo Bonds and Bail–in guides the reader through the different structures and their particular risks. Starting with an introduction to convertible bonds, the book covers bail–in capital and contingent convertibles (CoCo Bonds). Basel III, the new regulatory framework that has been driving these new developments is discussed as well. The price dynamics and valuation of CoCo bonds are presented in a practical way, using a Black Scholes  approach,  a Constant Elasticity of Variance (CEV) framework, American Monte Carlo techniques, to name a few. The Handbook of Hybrid Securities offers a quantitative and practical approach for readers at all levels of experience. The book is ideal for the absolute beginner wishing to familiarise themselves with this asset class and its regulatory context.  For more advanced users, working in areas such as trading, portfolio and risk management, the book provides a detailed introduction to the latest advances in numerical techniques in order to value and hedge these instruments.

Reading this Book Acknowledgments 1 Hybrid Assets 1.1 Introduction 1.2 Hybrid Capital 1.3 Preferreds 1.4 Convertible Bonds 1.5 Contingent Convertibles 1.6 Other Types of Hybrid Debt 1.6.1 Hybrid Bank Capital 1.6.2 Hybrid Corporate Capital 1.6.3 Toggle Bonds 1.7 Regulation 1.7.1 Making Failures Less Likely 1.7.2 Making Failures Less Disruptive 1.8 Bail–In Capital 1.9 Risk and Rating 1.9.1 Risk 1.9.2 Rating 1.10 Conclusion 2 Convertible Bonds 2.1 Introduction 2.2 Anatomy of a Convertible Bond 2.2.1 Final Payoff 2.2.2 Price Graph 2.2.3 Quotation of a Convertible Bond 2.2.4 Bond Floor ( ) 2.2.5 Parity 2.2.6 Convexity 2.2.7 Optional Conversion 2.2.8 Forced Conversion 2.2.9 Mandatory Conversion 2.3 Convertible Bond Arbitrage 2.3.1 Components of Risk 2.3.2 Delta 2.3.3 Delta Hedging 2.3.4 Different Notions of Delta 2.3.5 Greeks 2.4 Standard Features 2.4.1 Issuer Call 2.4.2 Put 2.4.3 Coupons 2.4.4 Dividends 2.5 Additional Features 2.5.1 Dividend Protection 2.5.2 Take–Over Protection 2.5.3 Refixes 2.6 Other Convertible Bond Types 2.6.1 Exchangeables 2.6.2 Synthetic Convertibles 2.6.3 Cross–Currency Convertibles 2.6.4 Reverse Convertibles 2.6.5 Convertible Preferreds 2.6.6 Make–Whole 2.6.7 Contingent Conversion 2.6.8 Convertible Bond Option 2.7 Convertible Bond Terminology 2.7.1 144A 2.7.2 Fixed–Income Metrics 2.8 Convertible Bond Market 2.8.1 Market Participants 2.8.2 Investors 2.9 Conclusion 3 Contingent Convertibles (CoCos) 3.1 Introduction 3.2 Definition 3.3 Anatomy 3.3.1 Loss–Absorption Mechanism 3.3.2 Trigger 3.3.3 Host Instrument 3.4 CoCos and Convertible Bonds 3.4.1 Forced vs. Optional Conversion 3.4.2 Negative vs. Positive Convexity 3.4.3 Limited vs. Unlimited Upside 3.4.4 Similarity to Reverse Convertibles 3.5 CoCos and Regulations 3.5.1 Introduction 3.5.2 Basel Framework 3.5.3 Basel I 3.5.4 Basel II 3.5.5 Basel III 3.5.6 CoCos in Basel III 3.5.7 High and Low–Trigger CoCos 3.6 Ranking in the Balance Sheet 3.7 Alternative Structures 3.8 Contingent Capital: Pro and Contra 3.8.1 Advantages 3.8.2 Disadvantages 3.8.3 Conclusion 4 Corporate Hybrids 4.1 Introduction 4.2 Issuer of Hybrid Debt 4.3 Investing in Hybrid Debt 4.4 Structure of a Corporate Hybrid Bond 4.4.1 Coupons 4.4.2 Replacement Capital Covenant 4.4.3 Issuer Calls 4.5 View of Rating Agencies 4.6 Risk in Hybrid Bonds 4.6.1 Subordination Risk 4.6.2 Deferral Risk 4.6.3 Extension Risk 4.7 Convexity in Hybrid Bonds 4.7.1 Case Study: Henkel 5.375% 2104 4.7.2 Duration Dynamics 4.8 Equity Character of Hybrid Bonds 5 Bail–In Bonds 5.1 Introduction 5.2 Definition 5.3 Resolution Regime 5.3.1 Resolution Tools 5.3.2 Timetable 5.4 Case Studies 5.4.1 Bail–In of Senior Bonds 5.4.2 Saving Lehman Brothers 5.5 Consequences of Bail–In 5.5.1 Higher Funding Costs 5.5.2 Higher GDP 5.5.3 Availability of Bail–In Bonds 5.5.4 Paying Bankers in Bail–In Bonds 5.6 Conclusion 6 Modeling Hybrids: An Introduction 6.1 Introduction 6.2 Heuristic Approaches 6.2.1 Corporate Hybrids: Yield of a Callable Bond 6.2.2 Convertible Bonds: Break Even 6.3 Building Models 6.3.1 Introduction 6.3.2 Martingales 6.3.3 Model Map 6.3.4 Cheapness 6.4 How Many Factors? 6.5 Sensitivity Analysis 6.5.1 Introduction 6.5.2 Non–linear Model 7 Modeling Hybrids: Stochastic Processes 7.1 Introduction 7.2 Probability Density Functions 7.2.1 Introduction 7.2.2 Normal Distribution 7.2.3 Lognormal Distribution 7.2.4 Exponential Distribution 7.2.5 Poisson Distribution 7.3 Brownian Motion 7.4 Ito Process 7.4.1 Introduction 7.4.2 Ito’s Lemma 7.4.3 Share Prices as Geometric Brownian Motion 7.5 Poisson Process 7.5.1 Definition 7.5.2 Advanced Poisson Processes 7.5.3 Conclusion 8 Modeling Hybrids: Risk Neutrality 8.1 Introduction 8.2 Closed–Form Solution 8.2.1 Introduction 8.2.2 Black–Scholes Solution 8.2.3 Solving the Black–Scholes Equation 8.2.4 Case Study: Reverse Convertible 8.3 Tree–Based Methods 8.3.1 Introduction 8.3.2 Framework 8.3.3 Geometry of the Trinomial Tree 8.3.4 Modeling Share Prices on a Trinomial Tree 8.3.5 European Options on a Trinomial Tree 8.3.6 American Options 8.3.7 Bermudan Options: Imposing a Particular Time Slice 8.4 Finite Difference Technique 8.5 Monte Carlo 8.5.1 Introduction 8.5.2 Generating Random Numbers 9 Modeling Hybrids: Advanced Issues 9.1 Tail Risk in Hybrids 9.2 Jump Diffusion 9.2.1 Introduction 9.2.2 Share Price Process with Jump to Default 9.2.3 Trinomial Trees with Jump to Default 9.2.4 Pricing Convertible Bonds with Jump Diffusion 9.2.5 Lost in Translation 9.3 Correlation 9.3.1 Correlation Risk in Hybrids 9.3.2 Definition 9.3.3 Correlating Wiener Processes 9.3.4 Cholesky Factorization 9.3.5 Cholesky Example 9.3.6 Correlating Events 9.3.7 Using Equity Correlation 9.3.8 Case Study: Correlated Defaults 9.3.9 Case Study: Asset Correlation vs. Default Correlation 9.4 Structural Models 9.5 Conclusion 10 Modeling Hybrids: Handling Credit 10.1 Credit Spread 10.1.1 Definition 10.1.2 Working with Credit Spreads 10.1.3 Option–Adjusted Spread 10.2 Default Intensity 10.2.1 Introduction 10.3 Credit Default Swaps 10.3.1 Definition 10.3.2 Example of a CDS Curve 10.3.3 Availability of CDS Data 10.3.4 Premium and Credit Leg 10.3.5 Valuation 10.3.6 Rule of Thumb 10.3.7 Market Convention 10.3.8 Case Study: Implied Default Probability 10.4 Credit Triangle 10.4.1 Definition 10.4.2 Case Study 10.4.3 The Big Picture 10.5 Stochastic Credit 11 Constant Elasticity of Variance 11.1 From Black–Scholes to CEV 11.1.1 Introduction 11.1.2 Leverage Effect 11.1.3 Link with Black–Scholes 11.2 Historical Parameter Estimation 11.3 Valuation: Analytical Solution 11.3.1 Moving Away from Black–Scholes 11.3.2 Semi–Closed–Form Formula 11.3.3 Numerical Example 11.4 Valuation: Trinomial Trees for CEV 11.4.1 American Options 11.4.2 Trinomial Trees for CEV 11.4.3 Numerical Example 11.5 Jump–Extended CEV Process 11.5.1 Introduction 11.5.2 JDCEV–Generated Skew 11.5.3 Convertible Bonds Priced under JDCEV 11.6 Case Study: Pricing Mandatories with CEV 11.6.1 Mandatory Conversion 11.6.2 Numerical Example 11.7 Case Study: Pricing Convertibles with a Reset 11.7.1 Refixing the Conversion Price 11.7.2 Involvement of CEV 11.7.3 Numerical Example 11.8 Calibration of CEV 11.8.1 Introduction 11.8.2 Local or Global Calibration 11.8.3 Calibrating CEV: Step by Step 12 Pricing Contingent Debt 12.1 Introduction 12.2 Credit Derivatives Method 12.2.1 Introduction 12.2.2 Loss 12.2.3 Trigger Intensity ( Trigger ) 12.2.4 CoCo Spread Calculation Example 12.2.5 Case Study: Lloyds Contingent Convertibles 12.3 Equity Derivatives Method 12.3.1 Introduction 12.3.2 Step 1: Zero–Coupon CoCo 12.3.3 Step 2: Adding Coupons 12.3.4 Numerical Example 12.3.5 Case Study: Lloyds Contingent Convertibles 12.3.6 Case Study: Tier 1 and Tier 2 CoCos 12.4 Coupon Deferral 12.5 Using Lattice Models 12.6 Linking Credit to Equity 12.6.1 Introduction 12.6.2 Hedging Credit Through Equity 12.6.3 Credit Elasticity 12.7 CoCos with Upside: CoCoCo 12.7.1 Downside Balanced with Upside 12.7.2 Numerical Example 12.8 Adding Stochastic Credit 12.8.1 Two–Factor Model 12.8.2 Monte Carlo Method 12.8.3 Pricing CoCos in a Two–Factor Model 12.8.4 Case Study 12.9 Avoiding Death Spirals 12.10 Appendix: Pricing Contingent Debt on a Trinomial Tree 12.10.1 Generalized Procedure 12.10.2 Positioning Nodes on the Trigger 12.10.3 Solving the CoCo Price 13 Multi–Factor Models for Hybrids 13.1 Introduction 13.2 Early Exercise 13.3 American Monte Carlo 13.3.1 Longstaff and Schwartz (LS) Technique 13.3.2 Convergence 13.3.3 Example: Longstaff and Schwartz (LS) Step by Step 13.3.4 Adding Calls and Puts 13.4 Multi–Factor Models 13.4.1 Adding Stochastic Interest Rates 13.4.2 Equity–Interest Rate Correlation 13.4.3 Adapting Longstaff and Schwartz (LS) 13.4.4 Convertible Bond under Stochastic Interest Rates 13.4.5 Adding Investor Put 13.5 Conclusion References Index

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.