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