Understanding Credit Derivatives and Related Instruments

Part I Credit Derivatives: Definition, Market, Uses 1 Credit Derivatives: A Brief Overview 1.1 What are Credit Derivatives?1.2 Potential \Gains from Trade" 1.3 Types of Credit Derivatives 1.3.1 Single-Name Instruments 1.3.2 Multi-Name Instruments1.3.3 Credit-Linked Notes 1.3.4 Sovereign vs. Other Reference Entities 1.4 Valuation Principles 1.4.1 Fundamental Factors 1.4.2 Other Potential Risk Factors1.4.3 Static Replication vs. Modeling1.4.4 A Note on Supply, Demand, and Market Frictions1.5 Counterparty Credit Risk (Again)2 The Credit Derivatives Market 2.1 Evolution and Size of the Market2.2 Market Activity and Size by Instrument Type2.2.1 Single- vs. Multi-name Instruments 2.2.2 Sovereign vs. Other Reference Entities 2.2.3 Credit Quality of Reference Entities2.2.4 Maturities of Most Commonly Negotiated Contracts2.3 Main Market Participants2.3.1 Buyers and Sellers of Credit Protection2.4 Common Market Practices 2.4.1 A First Look at Documentation Issues 2.4.2 Collateralization and Netting 3 Main Uses of Credit Derivatives 3.1 Credit Risk Management by Banks 3.2 Managing Bank Regulatory Capital 3.2.1 A Brief Digression: The 1988 Basle Accord 3.2.2 Credit Derivatives and Regulatory Capital Management3.3 Yield Enhancement, Portfolio Diversi_cation 3.3.1 Leveraging Credit Exposure, Unfunded Instruments3.3.2 Synthesizing Long Positions in Corporate Debt 3.4 Shorting Corporate Bonds 3.5 Other uses of credit derivatives3.5.1 Hedging Vendor-_nanced Deals 3.5.2 Hedging by convertible bond investors 3.5.3 Selling Protection as an Alternative to Loan Origination 3.6 Credit Derivatives as Market IndicatorsPart II Main Types of Credit Derivatives 4 Floating-Rate Notes 4.1 Not a Credit Derivative4.2 How Does It Work? 4.3 Common Uses 4.4 Valuation Considerations5 Asset Swaps 5.1 A Borderline Credit Derivative5.2 How Does It Work? 5.3 Common Uses 5.4 Valuation Considerations 5.4.1 Valuing the two pieces of an asset swap 5.4.2 Comparison to Par Floaters 6 Credit Default Swaps 6.1 How Does It Work?6.2 Common Uses 6.2.1 Protection Buyers 6.2.2 Protection Sellers6.2.3 Some Additional Examples 6.3 Valuation Considerations 6.3.1 CDS vs. Cash Spreads in Practice 6.3.2 A Closer Look at the CDS-Cash Basis 6.3.3 When Cash Spreads are Unavailable6.4 Variations on the Basic Structure 7 Total Return Swaps 7.1 How Does It Work? 7.2 Common Uses 7.3 Valuation Considerations 7.4 Variations on the Basic Structure8 Spread and Bond Options 8.1 How Does It Work?8.2 Common Uses8.3 Valuation Considerations 8.4 Variations on Basic Structures 9 Basket Default Swaps 9.1 How Does It Work? 9.2 Common Uses 9.3 Valuation Considerations9.3.1 A first look at default correlation 9.4 Variations on the Basic Structure10 Portfolio Default Swaps 12910.1 How Does It Work? 10.2 Common Uses 10.3 Valuation Considerations10.3.1 A _rst look at the loss distribution function 10.3.2 Loss distribution and default correlation 10.4 Variations on the Basic Structure 11 Principal-Protected Structures 11.1 How Does It Work? 11.2 Common Uses 11.3 Valuation Considerations 11.4 Variations on the Basic Structure 12 Credit-Linked Notes 12.1 How Does It Work? 12.2 Common Uses 12.3 Valuation Considerations 12.4 Variations on the Basic Structure 13 Repackaging Vehicles13.1 How Does It Work? 13.2 Why Use Repackaging Vehicles?13.3 Valuation Considerations13.4 Variations on the Basic Structure 14 Synthetic CDOs 16114.1 Traditional CDOs 14.1.1 How Does it Work? 14.1.2 Common Uses 14.1.3 Valuation Considerations 14.2 Synthetic Securitization 14.2.1 Common uses: Why go synthetic?14.2.2 Valuation considerations for synthetic CDOs 14.2.3 Variations on the Basic StructureIII Introduction to Credit Modeling I: Single-Name Defaults 15 Valuing Defaultable Bonds 15.1 Zero-coupon Bonds 15.2 Risk-neutral Valuation and Probability 15.2.1 Risk-neutral probabilities15.3 Coupon-paying Bonds15.4 Nonzero Recovery15.5 Risky Bond Spreads 15.6 Recovery Rates 16 The Credit Curve 16.1 CDS-implied Credit Curves16.1.1 Implied Survival Probabilities 16.1.2 Examples 16.1.3 Flat CDS Curve Assumption 16.1.4 A Simple Rule of Thumb 16.1.5 Sensitivity to Recovery Rate Assumptions16.2 Marking to Market a CDS Position16.3 Valuing a Principal-protected Note 16.3.1 Examples 16.3.2 PPNs vs. Vanilla Notes16.4 Other Applications and Some Caveats 17 Main Credit Modeling Approaches 17.1 Structural Approach 17.1.1 The Black-Scholes-Merton Model 17.1.2 Solving the Black-Scholes-Merton Model 17.1.3 Practical Implementation of the Model 17.1.4 Extensions and Empirical Validation 17.1.5 Credit Default Swap Valuation17.2 Reduced-Form Approach17.2.1 Overview of Some Important Concepts 17.2.1.1 Stochastic interest rates 17.2.1.2 Forward default probabilities 17.2.1.3 Forward default rates17.2.2 Uncertain Time of Default 17.2.3 Default Intensity 17.2.4 Pricing Defaultable Bonds 17.2.4.1 Non-zero recovery 17.2.4.2 Alternative recovery assumptions 17.2.5 Extensions and Uses of Reduced-form Models 17.2.6 Credit Default Swap Valuation 17.3 Comparing the Two Main Approaches 17.4 Ratings-based Models 18 Valuing of Credit Options 18.1 Forward-starting contracts 18.1.1 Valuing a Forward-starting CDS 18.1.2 Other forward-starting structures18.2 Valuing Credit Default Swaptions 18.3 Valuing other Credit Options 18.4 Alternative Valuation Approaches 18.5 Valuing Bond OptionsIV Introduction to Credit Modeling II: Portfolio Credit Risk19 The Basics of Portfolio Credit Risk 19.1 Default Correlation 19.1.1 Pairwise default correlation 19.1.2 Modeling default correlation 19.1.3 Pairwise default correlation and \_" 19.2 The Loss Distribution Function 19.2.1 Conditional loss distribution function19.2.2 Unconditional loss distribution function 19.2.3 Large-portfolio approximation 19.3 Default Correlation and Loss Distribution19.4 Monte Carlo Simulation: Brief Overview 19.4.1 How Accurate is the Simulation-Based Method?19.4.2 Evaluating the Large-Portfolio Method 19.5 Conditional vs. Unconditional Loss Distributions19.6 Other Approaches to Portfolio Credit Risk Modeling20 Valuing Basket Default Swaps 20.1 Basic Features of Basket Swaps 20.2 Reexamining the Two-Asset FTD Basket 20.3 FTD Basket with Several Reference Entities 20.3.1 A simple numerical example 20.3.2 A more realistic valuation exercise20.4 The Second-to-Default Basket 20.5 Basket Valuation and Asset Correlation20.6 Extensions and Alternative Approaches21 Valuing Portfolio Swaps and CDOs 21.1 A Simple Numerical Example 21.2 Model-based Valuation Exercise 21.3 The E_ects of Asset Correlation 21.4 The Large-Portfolio Approximation 21.5 Valuing CDOs: Some basic insights 21.5.1 Special considerations for CDO valuation21.6 Concluding Remarks 22 A Quick Tour of Commercial Models 22.1 CreditMetrics 22.2 The KMV Framework22.3 CreditRisk+22.4 Moody’s Binomial Expansion Technique 22.5 Intensity-based Models22.6 Concluding Thoughts23 Modeling Counterparty Credit Risk 23.1 The Single-Name CDS as a \Two-Asset Portfolio"23.2 The Basic Model23.3 A CDS with No Counterparty Credit Risk23.4 A CDS with Counterparty Credit Risk 23.4.1 Analytical derivation of joint probabilities of default 23.4.2 Simulation-based approach 23.4.3 An Example23.5 Other Models and Approaches23.6 Counterparty Credit Risk in Multiname StructuresV A Brief Overview of Documentation and Regulatory Issues 24 Anatomy of a CDS Transaction 24.1 Standardization of CDS Documentation24.1.1 Essential terms of a CDS transaction24.1.1.1 The reference entity 24.1.1.2 Reference and deliverable obligations24.1.1.3 Settlement method24.1.1.4 Credit events 24.1.2 Other important details of a CDS transaction24.2 When a Credit Event Takes Place24.2.1 Credit event noti_cation and veri_cation24.2.2 Settling the contract24.3 The Restructuring Debate 24.3.1 A case in point: Conseco 24.3.2 Modi_ed Restructuring24.3.3 A Bifurcated Market24.4 Valuing the Restructuring Clause 24.4.1 Implications for implied survival probabilities25 A Primer on Bank Regulatory Issues 25.1 The Basel II Capital Accord 25.2 Basel II Risk Weights and Credit Derivatives25.3 Suggestions for Further Reading Appendix A Basic Concepts from Bond Math A.1 Zero-coupon Bonds A.2 Compounding A.3 Zero-coupon Bond Prices as Discount Factors A.4 Coupon-paying Bonds A.5 Inferring Zero-coupon Yields from the Coupon Curve A.6 Forward Rates A.7 Forward Interest Rates and Bond PricesAppendix B Basic Concepts from Statistics B.1 Probability Density Function: Discrete Case B.2 Cumulative Distribution Function B.3 Probability Density Function: Continuous Case B.4 Expected Value and Variance B.5 Bernoulli Trials and the Bernoulli Distribution B.6 The Binomial Distribution B.7 The Poisson and Exponential Distributions B.8 The Normal DistributionB.9 The Lognormal Distribution B.10 Joint Probability Distributions B.11 Independence B.12 The Bivariate Normal Distribution