The Handbook of Hybrid Securities -- Contents -- 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 (BF) -- 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 (λTrigger) -- 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.