Handbook of Hybrid Securities

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.

• Reading this Book xvAcknowledgments xvii1 Hybrid Assets 11.1 Introduction 11.2 Hybrid Capital 11.3 Preferreds 31.4 Convertible Bonds 51.5 Contingent Convertibles 71.6 Other Types of Hybrid Debt 71.6.1 Hybrid Bank Capital 71.6.2 Hybrid Corporate Capital 131.6.3 Toggle Bonds 141.7 Regulation 151.7.1 Making Failures Less Likely 151.7.2 Making Failures Less Disruptive 151.8 Bail-In Capital 161.9 Risk and Rating 171.9.1 Risk 171.9.2 Rating 181.10 Conclusion 182 Convertible Bonds 192.1 Introduction 192.2 Anatomy of a Convertible Bond 222.2.1 Final Payoff 222.2.2 Price Graph 222.2.3 Quotation of a Convertible Bond 232.2.4 Bond Floor (B F) 252.2.5 Parity 272.2.6 Convexity 272.2.7 Optional Conversion 332.2.8 Forced Conversion 352.2.9 Mandatory Conversion 352.3 Convertible Bond Arbitrage 372.3.1 Components of Risk 372.3.2 Delta 422.3.3 Delta Hedging 452.3.4 Different Notions of Delta 452.3.5 Greeks 462.4 Standard Features 472.4.1 Issuer Call 472.4.2 Put 502.4.3 Coupons 532.4.4 Dividends 562.5 Additional Features 582.5.1 Dividend Protection 582.5.2 Take-Over Protection 592.5.3 Refixes 602.6 Other Convertible Bond Types 622.6.1 Exchangeables 622.6.2 Synthetic Convertibles 632.6.3 Cross-Currency Convertibles 642.6.4 Reverse Convertibles 662.6.5 Convertible Preferreds 672.6.6 Make-Whole 672.6.7 Contingent Conversion 672.6.8 Convertible Bond Option 682.7 Convertible Bond Terminology 682.7.1 144a 682.7.2 Fixed-Income Metrics 682.8 Convertible Bond Market 732.8.1 Market Participants 732.8.2 Investors 742.9 Conclusion 763 Contingent Convertibles (CoCos) 773.1 Introduction 773.2 Definition 783.3 Anatomy 793.3.1 Loss-Absorption Mechanism 793.3.2 Trigger 833.3.3 Host Instrument 863.4 CoCos and Convertible Bonds 873.4.1 Forced vs. Optional Conversion 873.4.2 Negative vs. Positive Convexity 883.4.3 Limited vs. Unlimited Upside 893.4.4 Similarity to Reverse Convertibles 893.5 CoCos and Regulations 893.5.1 Introduction 893.5.2 Basel Framework 903.5.3 Basel I 913.5.4 Basel II 923.5.5 Basel III 933.5.6 Cocos in Basel III 1013.5.7 High and Low-Trigger CoCos 1043.6 Ranking in the Balance Sheet 1063.7 Alternative Structures 1063.8 Contingent Capital: Pro and Contra 1073.8.1 Advantages 1073.8.2 Disadvantages 1073.8.3 Conclusion 1104 Corporate Hybrids 1134.1 Introduction 1134.2 Issuer of Hybrid Debt 1134.3 Investing in Hybrid Debt 1144.4 Structure of a Corporate Hybrid Bond 1154.4.1 Coupons 1154.4.2 Replacement Capital Covenant 1184.4.3 Issuer Calls 1194.5 View of Rating Agencies 1214.6 Risk in Hybrid Bonds 1224.6.1 Subordination Risk 1224.6.2 Deferral Risk 1224.6.3 Extension Risk 1224.7 Convexity in Hybrid Bonds 1224.7.1 Case Study: Henkel 5.375% 2104 1224.7.2 Duration Dynamics 1264.8 Equity Character of Hybrid Bonds 1265 Bail-In Bonds 1275.1 Introduction 1275.2 Definition 1285.3 Resolution Regime 1295.3.1 Resolution Tools 1305.3.2 Timetable 1305.4 Case Studies 1335.4.1 Bail-In of Senior Bonds 1335.4.2 Saving Lehman Brothers 1345.5 Consequences of Bail-In 1365.5.1 Higher Funding Costs 1365.5.2 Higher GDP 1365.5.3 Availability of Bail-In Bonds 1365.5.4 Paying Bankers in Bail-In Bonds 1365.6 Conclusion 1376 Modeling Hybrids: An Introduction 1396.1 Introduction 1396.2 Heuristic Approaches 1406.2.1 Corporate Hybrids: Yield of a Callable Bond 1406.2.2 Convertible Bonds: Break Even 1426.3 Building Models 1436.3.1 Introduction 1436.3.2 Martingales 1456.3.3 Model Map 1466.3.4 Cheapness 1476.4 How Many Factors? 1496.5 Sensitivity Analysis 1526.5.1 Introduction 1526.5.2 Non-linear Model 1537 Modeling Hybrids: Stochastic Processes 1597.1 Introduction 1597.2 Probability Density Functions 1597.2.1 Introduction 1597.2.2 Normal Distribution 1607.2.3 Lognormal Distribution 1617.2.4 Exponential Distribution 1627.2.5 Poisson Distribution 1637.3 Brownian Motion 1647.4 Ito Process 1657.4.1 Introduction 1657.4.2 Ito’s Lemma 1667.4.3 Share Prices as Geometric Brownian Motion 1697.5 Poisson Process 1727.5.1 Definition 1727.5.2 Advanced Poisson Processes 1747.5.3 Conclusion 1768 Modeling Hybrids: Risk Neutrality 1778.1 Introduction 1778.2 Closed-Form Solution 1808.2.1 Introduction 1808.2.2 Black–Scholes Solution 1828.2.3 Solving the Black–Scholes Equation 1838.2.4 Case Study: Reverse Convertible 1848.3 Tree-Based Methods 1868.3.1 Introduction 1868.3.2 Framework 1878.3.3 Geometry of the Trinomial Tree 1898.3.4 Modeling Share Prices on a Trinomial Tree 1938.3.5 European Options on a Trinomial Tree 1998.3.6 American Options 2008.3.7 Bermudan Options: Imposing a Particular Time Slice 2038.4 Finite Difference Technique 2048.5 Monte Carlo 2058.5.1 Introduction 2058.5.2 Generating Random Numbers 2069 Modeling Hybrids: Advanced Issues 2119.1 Tail Risk in Hybrids 2119.2 Jump Diffusion 2129.2.1 Introduction 2129.2.2 Share Price Process with Jump to Default 2149.2.3 Trinomial Trees with Jump to Default 2179.2.4 Pricing Convertible Bonds with Jump Diffusion 2219.2.5 Lost in Translation 2269.3 Correlation 2279.3.1 Correlation Risk in Hybrids 2279.3.2 Definition 2289.3.3 Correlating Wiener Processes 2299.3.4 Cholesky Factorization 2309.3.5 Cholesky Example 2339.3.6 Correlating Events 2349.3.7 Using Equity Correlation 2359.3.8 Case Study: Correlated Defaults 2379.3.9 Case Study: Asset Correlation vs. Default Correlation 2389.4 Structural Models 2409.5 Conclusion 24210 Modeling Hybrids: Handling Credit 24310.1 Credit Spread 24310.1.1 Definition 24310.1.2 Working with Credit Spreads 24410.1.3 Option-Adjusted Spread 24610.2 Default Intensity 24610.2.1 Introduction 24610.3 Credit Default Swaps 24810.3.1 Definition 24810.3.2 Example of a CDS Curve 25010.3.3 Availability of CDS Data 25010.3.4 Premium and Credit Leg 25110.3.5 Valuation 25210.3.6 Rule of Thumb 25510.3.7 Market Convention 25610.3.8 Case Study: Implied Default Probability 25710.4 Credit Triangle 25910.4.1 Definition 25910.4.2 Case Study 26010.4.3 The Big Picture 26310.5 Stochastic Credit 26311 Constant Elasticity of Variance 26711.1 From Black–Scholes to CEV 26711.1.1 Introduction 26711.1.2 Leverage Effect 26811.1.3 Link with Black–Scholes 26911.2 Historical Parameter Estimation 27011.3 Valuation: Analytical Solution 27411.3.1 Moving Away from Black–Scholes 27411.3.2 Semi-Closed-Form Formula 27511.3.3 Numerical Example 27611.4 Valuation: Trinomial Trees for CEV 27711.4.1 American Options 27711.4.2 Trinomial Trees for CEV 27711.4.3 Numerical Example 27911.5 Jump-Extended CEV Process 28311.5.1 Introduction 28311.5.2 JDCEV-Generated Skew 28411.5.3 Convertible Bonds Priced under JDCEV 28411.6 Case Study: Pricing Mandatories with CEV 28611.6.1 Mandatory Conversion 28611.6.2 Numerical Example 28711.7 Case Study: Pricing Convertibles with a Reset 28811.7.1 Refixing the Conversion Price 28811.7.2 Involvement of CEV 29111.7.3 Numerical Example 29211.8 Calibration of CEV 29511.8.1 Introduction 29511.8.2 Local or Global Calibration 29611.8.3 Calibrating CEV: Step by Step 29612 Pricing Contingent Debt 30112.1 Introduction 30112.2 Credit Derivatives Method 30212.2.1 Introduction 30212.2.2 Loss 30212.2.3 Trigger Intensity (λ Trigger) 30312.2.4 CoCo Spread Calculation Example 30512.2.5 Case Study: Lloyds Contingent Convertibles 30512.3 Equity Derivatives Method 30712.3.1 Introduction 30712.3.2 Step 1: Zero-Coupon CoCo 30812.3.3 Step 2: Adding Coupons 30912.3.4 Numerical Example 31112.3.5 Case Study: Lloyds Contingent Convertibles 31312.3.6 Case Study: Tier 1 and Tier 2 CoCos 31612.4 Coupon Deferral 31712.5 Using Lattice Models 32112.6 Linking Credit to Equity 32312.6.1 Introduction 32312.6.2 Hedging Credit Through Equity 32612.6.3 Credit Elasticity 32612.7 CoCos with Upside: CoCoCo 32912.7.1 Downside Balanced with Upside 32912.7.2 Numerical Example 33012.8 Adding Stochastic Credit 33312.8.1 Two-Factor Model 33312.8.2 Monte Carlo Method 33512.8.3 Pricing CoCos in a Two-Factor Model 33712.8.4 Case Study 33812.9 Avoiding Death Spirals 33912.10 Appendix: Pricing Contingent Debt on a Trinomial Tree 34112.10.1 Generalized Procedure 34112.10.2 Positioning Nodes on the Trigger 34312.10.3 Solving the CoCo Price 34513 Multi-Factor Models for Hybrids 34713.1 Introduction 34713.2 Early Exercise 34813.3 American Monte Carlo 35213.3.1 Longstaff and Schwartz (LS) Technique 35213.3.2 Convergence 35613.3.3 Example: Longstaff and Schwartz (LS) Step by Step 35613.3.4 Adding Calls and Puts 36213.4 Multi-Factor Models 36413.4.1 Adding Stochastic Interest Rates 36413.4.2 Equity–Interest Rate Correlation 36513.4.3 Adapting Longstaff and Schwartz (LS) 36613.4.4 Convertible Bond under Stochastic Interest Rates 36713.4.5 Adding Investor Put 37113.5 Conclusion 371References 373Index 381

“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)