Credit Derivatives

GEOFF CHAPLIN studied mathematics at Cambridge (MA 1972) and Oxford (MSc 1973, DPhil 1975) and trained as an actuary (FFA 1978) while working in a life insurance company. He moved to the City in 1980 and has worked for major banks (including HSBC, Nomura International, and ABN AMRO). As a partner in Reoch Credit he has consulted to law firms, hedge funds, corporate treasurers, institutional investment funds and risk control departments of major banks in the areas of credit and mortality risk. He has been involved in the credit derivatives market since 1996 and life settlements structures since 2003. Geoff has also maintained strong academic interests – he was a visiting (emeritus) professor at the University of Waterloo, Canada, from 1987 until 1999. He has also published many articles in Risk, the Journal of the Institute and Faculty of Actuaries, and others, speaks regularly at conferences and is the author of Credit Derivatives: Risk Management, Trading and Investing (John Wiley & Sons Ltd, 2005) and co-author of Life Settlements and Longevity Structures: Pricing and Risk Management: Investment and Structured Finance (John Wiley & Sons Ltd, 2009).

• Preface to the First Edition xviiPreface to the Second Edition xixAcknowledgements xxiDisclaimer xxiiiTable of Spreadsheet Examples and Software xxviiAbout the Author xxixPart I Credit Background and Credit Derivatives 11 Credit Debt and Other Traditional Credit Instruments 31.1 Bonds and Loans; Libor Rates and Swaps; ‘REPO’ and General Collateral Rates 31.1.1 Bonds and Loans 31.1.2 BBA Libor and Swaps 41.1.3 Collateralised Lending and Repo 41.1.4 Repo as a Credit Derivative 61.2 Credit Debt Versus ‘Risk-Free’ Debt 61.3 Issue Documents, Seniority and the Recovery Process 61.3.1 Issue Documents and Default 61.3.2 Claim Amount 71.3.3 The Recovery Process and Recovery Amount 81.3.4 Sovereign versus Corporate Debt 91.4 Valuation, Yield and Spread 101.5 Buying Risk 101.6 Marking to Market, Marking to Model and Reserves 111.7 The ‘Credit Crunch’ and Correlation 121.8 Parties Involved in the Credit Markets and Key Terminology 132 Default and Recovery Data; Transition Matrices; Historical Pricing 152.1 Recovery: Ultimate and Market-Value-Based Recovery 152.1.1 Ultimate Recovery 152.1.2 Market Recovery 162.1.3 Recovery Rates and Industry Sector 182.1.4 Recovery and Default Rates and the Economic Cycle 182.1.5 Modelling Recovery Rates 182.2 Default Rates: Rating and Other Factors 212.3 Transition Matrices 212.4 ‘Measures’ and Transition Matrix-Based Pricing 222.5 Spread Jumps and Spread Volatility Derived from Transition Matrices 262.6 Adjusting Transition Matrices 273 Asset Swaps and Asset Swap Spread; z-Spread 293.1 ‘Par–Par’ Asset Swap Contracts 293.1.1 Contract Description and Hedging 293.1.2 Hedging 293.1.3 Default of the Reference Name 303.2 Asset Swap Spread 303.3 Maturity and z-Spread 303.4 Callable Asset Swaps; ‘Perfect’ Asset Swaps 323.4.1 Callable Asset Swaps 333.4.2 ‘Perfect’ Asset Swaps 333.5 A Bond Spread Model 334 Liquidity, the Credit Pyramid and Market Data 354.1 Bond Liquidity 354.2 The Credit Pyramid 354.3 Engineered and Survey Data 374.3.1 Survey Data 374.3.2 Engineered Data 384.4 Spread and Rating 395 Traditional Counterparty Risk Management 415.1 Vetting 415.2 Collateralisation and Netting 415.3 Additional Counterparty Requirements for Credit Derivative Counterparties 425.4 Internal Capital Charge 426 Credit Portfolios and Portfolio Risk 436.1 VaR and counterpartyVaR 436.2 Distribution of Forward Values of a Credit Bond 436.3 Correlation and the Multi-Factor Normal (Gaussian) Distribution 456.4 Correlation and the Correlation Matrix 467 Introduction to Credit Derivatives 497.1 Products and Users 497.1.1 ‘Traditional’ Credit Instruments 497.1.2 ‘Single Name’ Credit Derivatives 497.1.3 Credit-Linked Notes 507.1.4 Portfolio Credit Derivatives 507.2 Market Participants and Market Growth 51Part II Credit Default Swaps and other Single Name Products 558 Credit Default Swaps; Product Description and Simple Applications 578.1 CDS Product Definition 578.1.1 Contract Description and Example 578.1.2 Market CDS Quotes and Premium Payment 588.1.3 Related Products 598.1.4 CDS on Loans: LCDS 608.2 Documentation 608.2.1 ISDA Documentation and Insurance Contract Differences 608.2.2 Reference Obligations, ‘Markit RED’ and CreditIDs 638.3 Credit Triggers for Credit Derivatives 658.3.1 Credit Events 658.3.2 Restructuring 668.4 CDS Applications and Elementary Strategies 678.4.1 Single Names 678.4.2 Sector/Portfolio Trades 688.4.3 Income Generation 698.4.4 Regulatory Capital Reduction 708.5 Counterparty Risk: PFE for CDS 718.6 CDS Trading Desk 718.6.1 Mechanics of Transacting a CDS Deal 718.6.2 Trade Monitoring, Credit Events, Unwinds 728.6.3 CDS Desk Interactions and Organisation 738.7 CDS Contract and Convention Changes 2009 738.7.1 Credit Derivatives: Review 738.7.2 Overview of Recent Changes 748.7.3 Contract Changes 748.7.4 Convention Changes 799 Valuation and Risk: Basic Concepts and the Default and Recovery Model 819.1 The Fundamental Credit Arbitrage – Repo Cost 819.2 Default and Recovery Model; Claim Amount 829.2.1 Claim Amount 829.2.2 Recovery Modelling 839.2.3 Hazard (Default) Rate Model 859.2.4 Choice of Hazard Rate Function/Interpolation Process 859.3 Deterministic Default Rate Model 879.3.1 CDS Valuation 889.3.2 Accrued Interest and the Delivery Option 909.3.3 CDS Under Constant Hazard Rate 919.3.4 Up-front Premiums 919.3.5 Bond Valuation 919.3.6 Bond Price Under a Constant Hazard Rate 929.3.7 Limiting Cases of the Bond Price 929.3.8 Risky Zero Coupon Bonds 939.3.9 CDS and Bond Sensitivities 939.4 Stochastic Default Rate Model; Hazard and Pseudo-Hazard Rates 949.5 Calibration to Market Data 979.5.1 Calibrating to CDSs and to Bonds 979.5.2 Implied Hazard Rates 989.5.3 Calibrating to Bonds: Multiple Solutions for the Hazard Rate 989.5.4 Calibrating to Bonds: Implied Recovery and Hazard Rates 989.5.5 Implied Hazard Rate Curve and No-Arbitrage 1019.5.6 Syndicated Loans 1019.6 CDS Data/Sources 1029.6.1 Survey Data 1029.6.2 Data Engineering 1049.7 Model Errors and Tests 1059.7.1 Recovery Assumption 1059.7.2 Interest and Hazard Rate Correlation 1069.7.3 Reference Name and Counterparty Hazard Rate Correlation 1069.7.4 Interpolation Assumptions, and the Pseudo-Hazard Rate versus Stochastic Hazard Rate 1089.8 CDS Risk Factors; Reserves and Model Risk 1089.8.1 Captured and Hidden Risks 1089.8.2 Limits 1099.8.3 Reserves against Implementation Errors 1099.8.4 Model Reserves 11110 CDS Deal Examples 11310.1 A CDS Hedged Against Another CDS 11310.1.1 Cross-Currency Default Swap Pricing and Hedging 11310.1.2 Back-to-Back Trades, Default Event Hedges and Curve Trades 11810.1.3 Hedging Both Credit Event and Spread Risk Simultaneously 12010.1.4 Seniority Mismatch 12210.1.5 Trade Level Hedging and Book Basis Hedging 12310.2 Introduction to Bond Hedging 12410.2.1 Default Event Hedging 12410.2.2 Spread Hedging 12510.2.3 Convertible Bonds and Equity Risk 12510.3 Hedge and Credit Event Examples 12611 CDS/Bond Basis Trading 13111.1 Bond Versus CDS: Liquidity 13111.2 Bond Repo Cost 13211.3 Bond Spread Measurement – z-Spread not Asset Swap Spread 13311.4 Bond Price Impact 13311.5 Embedded Options in Bonds and Loans 13411.6 Delivery Option in CDSs 13511.7 Payoff of Par 13611.8 Trigger Event Differences 13611.9 Embedded Repo Option 13711.10 Putting it All Together 13812 Forward CDS; Back-to-Back CDS, Mark to Market and CDS Unwind 13912.1 Forward CDS 13912.2 Mark-to-Market and Back-to-Back CDS 14012.3 Unwind Calculation; Off-Market Trade Valuation and Hedging 14112.4 ‘Double-Trigger CDS’ 14213 Credit-Linked Notes 14513.1 CLN Set-Up; Counterparty or Collateral Risk 14513.2 Embedded Swaps and Options 14713.3 Costs 14813.4 Applications 14813.5 CLN Pricing 14913.5.1 Basic Pricing 14913.5.2 CLN Pricing Model 14913.6 Capital Guaranteed Note 15014 Digital or ‘Fixed Recovery’ CDS 15514.1 Product Description 15514.2 Pricing, Hedging, Valuation and Risk Calculations 15514.2.1 Simple Pricing 15514.2.2 Recovery Assumptions 15614.2.3 Valuation and Hedging 15614.3 Trigger Event Differences 15715 Spread Options, Callable/Puttable Bonds, Callable Asset Swaps, Callable Default Swaps 15915.1 Product Definitions 15915.1.1 Vanilla Spread Options and Variations 15915.1.2 Related Embedded Products 16015.1.3 Bond Price Options 16115.1.4 Applications 16215.2 Model Alternatives and a Stochastic Default Rate Model for Spread Option Pricing 16215.2.1 Model Approaches 16215.2.2 Hazard Rate Tree 16315.2.3 Callable High Yield Bonds 16415.3 Sensitivities and Hedging 16416 Total Return Swaps 16716.1 Product Definition and Examples 16716.2 Applications 16716.3 Hedging and Valuation 16816.3.1 Pricing and Hedging 16816.3.2 Valuation 16917 Single Name Book Management 17117.1 Risk Aggregation 17117.2 CreditVaR for CDSs 17318 CDS and Simulation 17518.1 The Poisson Model and Default Times 17518.2 Valuation by Monte Carlo Simulation 17518.3 Sensitivity 178Part III Portfolio Products 18119 Portfolio Product Types 18319.1 Nth-to-Default Baskets 18419.1.1 First-to-Default Product Definition and Example 18419.1.2 Documentation and Takeovers 18519.1.3 Second-(and Higher)-to-Default 18719.1.4 Applications 18719.2 ‘Synthetic’ CDOs 18819.2.1 Standard Indices: Markit iTraxx and Markit cdx 18819.2.2 Index Options and Modelling Spread 19219.2.3 CDO Structures on Standard Indices 19419.2.4 Bespoke Synthetic CDOs 19519.2.5 Managed Synthetic CDOs: Compliance Tests (OC and IC Tests; WARF; Diversity Score) and Substitutions 20019.2.6 CDO Squared 20319.2.7 Funded (CLN) and Unfunded (CDS) Tranches 20519.2.8 Relationship to nth-to-Default 20619.2.9 Applications 20719.2.10 Portfolio Optimisation 20819.3 Cashflow CDOs 21019.3.1 Reference Pools 21119.3.2 Income and Capital Waterfalls: Reserve Accounts 21119.3.3 Funding and SPVs 21319.3.4 Balance Sheet CDOs 21519.3.5 Diversification and Risk Reduction Trades; Credit Bank 21819.4 Credit Securitisations 22019.5 Rating 22219.6 Alternative Levered Credit Portfolio Products 22219.6.1 Cppi 22319.6.2 Cpdo 22419.6.3 Advantages of Market Value CDS Products 22620 The Normal Copula and Correlation 22720.1 Default Time Correlation 22720.1.1 Generating Correlated Default Times 22720.1.2 Intuitive Understanding of Default Time Correlation 22720.1.3 Implications of 100% Default Time Correlation 22920.1.4 N2D, Zero Correlation Case – Exact Pricing and Hedging Formulas 23020.1.5 N2D, 100% Correlation – Exact Pricing and Hedging Formulas 23420.1.6 N2D, Recovery Uncertainty 23520.2 Normal Copula 23620.2.1 Generating Correlated Default Times under the Normal Copula 23720.2.2 Correlation Types: Pairwise, Tag, Tranche/Compound and Base Correlation; Factor Correlation 23820.2.3 Simulation Pricing 23920.2.4 Variance Reduction Techniques 24220.2.5 Semi-Closed Form (SCF) Pricing 24220.3 Correlation 24420.3.1 Sources of Correlation 24420.3.2 Constraints: What Makes a Correlation Matrix? 24520.3.3 Spread Correlation 24620.3.4 Asset and Equity Correlation 24720.3.5 Estimation from Historical Data 24820.3.6 Factor Analysis and Factor Correlation; Tag Correlation 24820.3.7 Impact on Hedging of Using Historical or Implied Correlations 25120.3.8 Implied Correlation 25121 Correlation in Practice 25321.1 Tranche Correlation 25321.1.1 Valuation and Key Features 25321.1.2 Implied Tranche Correlation 25621.1.3 CDS Curve Adjustment 25721.1.4 Bid–Offer Impact 25721.2 Base Correlation 25721.2.1 Valuation and Key Features 25821.2.2 Implied Base Correlation 25921.2.3 Interpolating Base Correlation 26021.3 Correlated Recoveries 26121.4 Correlation Regime Change and Other Modelling Approaches 26221.4.1 Stochastic Correlation: Regime Change Models 26221.4.2 Spread Factor 26322 Valuation and Hedging 26522.1 Valuation Examples 26522.1.1 F2D Baskets 26522.1.2 CDO Pricing: Change of Correlation 26522.1.3 CDO Pricing: Change of Tranching 26722.1.4 CDO Pricing: Change of Underlying 26822.1.5 CDO Pricing: Change of Maturity 26922.1.6 Managed CDO: Substitution and Change of Subordination 26922.2 Sensitivity Calculation and Hedging 27022.2.1 Dynamic Hedging: Spread Risk 27122.2.2 Static Hedging: Default Event Risk 27722.2.3 Correlation Risk 27922.2.4 Recovery Risk 28022.2.5 Convexity Risks 28122.3 Pricing More Complex Structures 28222.3.1 CDO Squared 28222.3.2 Cashflow CDOs 28222.4 Model Errors and Tests; Alternative Models 28422.4.1 Captured and Hidden Risks 28422.4.2 Spread Models 28422.4.3 Reserves 28523 Alternative Copulas 28923.1 Student’s t-Distribution 28923.2 Copulas in General 29023.3 Archimedean Copulas: Clayton, Gumbel 29123.4 Clayton at θ = 0 and θ = ∞ 29323.5 Model Risk 29324 Correlation Portfolio Management 29724.1 Static and Dynamic Hedges 29724.2 Correlation Book Management 29824.3 CreditVaR and CounterpartyVaR 300Part IV Default Swaps Including Counterparty Risk 30325 Single Name CDS 30325.1 Non-Correlated Counterparty 30525.2 100% Correlation 30625.3 Correlated Counterparty: Pricing and Hedging 30825.4 Choice of Copula 30925.5 Collateralised Deals and CDS Book Management 30926 Counterparty CDSs 31326.1 Pricing 31326.2 Counterparty CDS (CCDS) Book Management 313Part V Systems Implementation and Testing 31727 Mathematical Model and Systems Validation 31927.1 Testing Procedures 31927.2 Implementation and Documentation 32128 System Implementation 32328.1 Anatomy of a CDO 32328.1.1 Reference Pool Data 32328.1.2 Tranche Data 32428.1.3 Deal Details 32428.2 Management 32528.2.1 What is Happening? 32528.2.2 What Has Happened? 32628.2.3 What is Likely to Happen and What is the Worst that can Happen? 32628.2.4 What Opportunities do I Have? 32728.2.5 Reporting 32828.2.6 Limits 32828.3 Valuation 32928.4 IT Considerations 33128.4.1 Why are Credit Derivatives Different? 33128.4.2 Spreadsheet 33228.4.3 Software Application 33228.4.4 Buy versus Build 333Part VI the Credit Crisis 33529 Cause and Effect: Credit Derivatives and the Crisis of 2007 33729.1 The Credit Markets Pre-Crisis 33729.1.1 Bank Motivation 33729.1.2 Fixed Income Investors 33829.1.3 Risk Traders versus Risk Absorbers 33829.1.4 Structured Investment Vehicles 33929.1.5 Market Liquidity 34029.2 The Events of MID- 2007 34129.2.1 Sub-prime Mortgages 34129.2.2 Investor Impact 34229.2.3 Bank Impact 34329.2.4 The Failure of Lehman Brothers and the Bailout of AIG 34529.3 Issues to be Addressed 34629.3.1 A Different Rating Agency Process 34629.3.2 Standardised Nomenclature for Credit Ratings 34729.3.3 Keeping a Percentage of Originated Risk on Balance Sheet 34829.3.4 Undrawn Credit Facility Capital Charge 34829.3.5 The Future of CDOs 34929.3.6 Mitigating the Negative Impact of Mark-to-Market 34929.4 Market Clearing Mechanisms 35029.4.1 Central Credit Counterparty 35129.4.2 Centralised Clearing and Systemic Risk 35129.4.3 A Dedicated CCP for CDSs Alone 35229.4.4 Conclusions 353Appendix Markit Credit and Loan Indices 355References 363Index 365