Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgements -- 1 A primer on collateralised debt obligations -- 1.1 Introduction -- 1.2 Securitisation and tranching -- 1.3 Credit derivative products -- 1.3.1 Credit default swaps (CDSs) -- 1.3.1.1 Forward starting CDSs -- 1.3.1.2 Credit default swaptions -- 1.3.1.3 Recovery rate plays -- 1.3.1.4 Constant maturity CDS (CMCDS) -- 1.3.2 Default baskets -- 1.3.3 Credit indices -- 1.3.4 Collateralised debt obligations (CDOs) -- 1.3.4.1 Cashflow CDOs -- 1.3.4.2 Synthetic CDOs -- 1.3.4.3 Single-tranche CDOs (STCDOs) -- 1.3.4.4 Options on index tranches -- 1.3.4.5 Tranchelets -- 1.3.4.6 Zero-coupon equity tranches -- 1.3.4.7 Structured investment vehicles (SIVs) -- 1.4 Chapter review -- 2 Modelling of obligor default -- 2.1 Introduction -- 2.2 Modelling single-name default as a Poisson process -- 2.2.1 The hazard rate model -- 2.2.2 Valuation of risky cashflows -- 2.3 Modelling default correlation-fundamental concepts -- 2.4 Introducing default dependence via copulas -- 2.4.1 Basic concepts -- 2.4.2 The Gaussian copula -- 2.4.3 The t copula -- 2.5 Rating transition methods for modelling obligor default -- 2.5.1 Formulation of the problem -- 2.5.2 Modelling rating transition dynamics -- 2.5.3 Determining risk-neutral transition probabilities -- 2.6 Chapter review -- 3 Valuation of credit default swaps -- 3.1 Introduction -- 3.2 Overview of vanilla credit default swaps -- 3.2.1 Description of the product -- 3.2.2 Cashflow mechanics -- 3.3 Valuation of vanilla CDSs -- 3.3.1 Valuing the fee leg -- 3.3.2 Valuing the contingent leg -- 3.3.3 Calculating the CDS PV -- 3.3.4 Calculating the CDS par spread -- 3.3.5 Calculating the CDS mark-to-market value -- 3.3.6 The credit triangle -- 3.3.7 Valuation via Monte Carlo simulation of obligor default times.

3.4 Calibration of the survival curve to market observed data -- 3.5 Risk sensitivities of vanilla CDSs -- 3.5.1 Counterparty risk -- 3.5.2 Recovery risk -- 3.5.3 Quantifying market risk - CS01s -- 3.5.4 Quantifying default risk - value-on-default (VoD) -- 3.6 Chapter review -- 4 Credit indices -- 4.1 Introduction -- 4.2 Description of the credit indices -- 4.3 Index trading mechanics -- 4.4 Valuation of credit indices -- 4.5 Time series analysis of credit indices -- 4.6 Tranched credit index exposures -- 4.7 Chapter review -- 5 Valuation of default baskets -- 5.1 Introduction -- 5.2 Brief overview of default baskets -- 5.3 General valuation principles for default baskets -- 5.4 Analytic valuation of default baskets in simple limiting cases -- 5.4.1 Valuation of first-to-default baskets (completely independent defaults) -- 5.4.2 Completely dependent defaults -- 5.5 Monte Carlo valuation of default baskets -- 5.5.1 Generating default time scenarios -- 5.5.2 Valuing cashflows -- 5.6 Phenomenology of default baskets -- 5.6.1 Baseline case to be analysed -- 5.6.2 Convergence of PV estimators -- 5.6.3 CDS par spread sensitivities -- 5.6.4 Correlation and basket maturity sensitivities -- 5.6.5 Impact of spread bump magnitude upon delta estimators -- 5.7 Semi-analytic valuation of default baskets -- 5.7.1 Approximating the full dependence structure within a factor model framework -- 5.7.2 A single-factor model -- 5.8 Chapter review -- 6 Valuation of synthetic CDOs -- 6.1 Introduction -- 6.2 Synthetic CDO cashflow mechanics -- 6.2.1 Tranche upfront payments and running spreads -- 6.2.2 Amortisation of the super-senior tranche -- 6.3 Basic principles of synthetic CDO pricing -- 6.4 Valuation in the standard market model using Monte Carlo simulation -- 6.5 Valuation in the standard market model using semi-analytic techniques.

6.5.1 The single-factor approximation to the full dependence structure -- 6.5.2 Constructing the portfolio loss distribution -- 6.5.2.1 A recursive method -- 6.5.2.2 Calculation of the marginal conditional obligor default probabilities -- 6.5.2.3 Calculation of the portfolio conditional loss distribution -- 6.5.2.4 Calculation of the tranche expected loss -- 6.5.2.5 The Fourier transform approach to computing the portfolio loss distribution -- 6.5.2.6 The normal proxy method -- 6.5.2.7 Approximating the portfolio loss distribution in the large portfolio limit -- 6.5.3 Default baskets revisited -- 6.6 Structural models -- 6.7 Chapter review -- 7 Phenomenology of the standard market model -- 7.1 Introduction -- 7.2 Baseline case analysed -- 7.3 Tranche loss statistics -- 7.4 Analysis of the portfolio loss distribution -- 7.4.1 Correlation dependence of the portfolio loss distribution -- 7.4.2 Maturity dependence -- 7.4.3 Portfolio expected loss as a function of time -- 7.5 Correlation and maturity sensitivity of the tranche par spread -- 7.5.1 Correlation sensitivity of the fee and contingent legs -- 7.5.2 Correlation sensitivity of the tranche par spread -- 7.5.3 Understanding tranche phenomenology -- 7.6 Default baskets revisited -- 7.7 Chapter review -- 8 Risk quantification of synthetic CDOs -- 8.1 Introduction -- 8.2 Synthetic CDO risk factors -- 8.2.1 Market risk factors -- 8.2.2 Credit risk factors -- 8.3 Baseline case analysed -- 8.4 Quantifying credit spread sensitivities-CS01 -- 8.4.1 Par spread sensitivity -- 8.4.2 Marginal CS01 -- 8.4.3 Multiple CS01 -- 8.5 Quantifying correlation sensitivities-correlation vega -- 8.6 Quantifying default risk sensitivities-value-on-default (VoD) -- 8.6.1 Marginal VoD -- 8.6.2 Multiple or running VoD -- 8.7 Tranche time decay -- 8.8 Credit spread value-at-risk (CVaR).

8.8.1 Evolving the spreads using historical data -- 8.8.2 Evolving the spreads using simulated data -- 8.9 Default value-at-risk (DVaR) -- 8.10 Chapter review -- 9 Implied and base correlations -- 9.1 Introduction -- 9.2 Market quoting conventions -- 9.3 The correlation smile and implied correlation -- 9.3.1 Why does the correlation smile exist? -- 9.3.2 What are the problems with implied correlation? -- 9.4 The market solution-base correlations -- 9.4.1 Computing base correlations -- 9.4.2 Valuation of bespoke tranches using the base correlation curve -- 9.5 Chapter review -- 10 Extensions of the standard market model -- 10.1 Introduction -- 10.2 Extending the standard market model -- 10.2.1 The mixed copula -- 10.2.2 The Student and double t copula -- 10.2.3 The normal inverse Gaussian (NIG) model -- 10.2.4 The functional copula -- 10.2.5 Stochastic correlation -- 10.2.6 Random factor loadings -- 10.2.7 Gamma process models -- 10.2.8 Levy base correlation -- 10.2.9 Other modelling approaches -- 10.3 Dynamic portfolio loss models -- 10.4 Chapter review -- 11 Exotic CDOs -- 11.1 Introduction -- 11.2 Synthetic CDO2 and CDOn -- 11.2.1 Valuation using Monte Carlo simulation -- 11.2.2 Valuation using semi-analytic methods -- 11.3 Cashflow CDOs -- 11.3.1 Description of cashflow CDOs -- 11.3.2 Example - a collateralised loan obligation -- 11.3.2.1 Modelling defaults -- 11.3.2.2 Modelling prepayments -- 11.3.2.3 The asset side -- 11.3.2.4 The liability side -- 11.3.2.5 Coverage tests -- 11.4 Asset backed CDS (ABCDS) -- 11.5 ABX indices and tranched ABX (TABX) exposures -- 11.5.1 ABX index and sub-indices -- 11.5.2 Tranched ABX (TABX) -- 11.6 Chapter review -- 12 Correlation trading of synthetic CDO tranches -- 12.1 Introduction -- 12.2 An overview of correlation trading -- 12.2.1 Definition of long/short correlation -- 12.2.2 Tranche leverage.

12.2.3 Single-tranche trading mechanics -- 12.2.4 Strategies to express specific views -- 12.2.4.1 Utilising tranche leverage with respect to indices -- 12.2.4.2 Relative value trades -- 12.2.4.3 Micro/macro hedging strategies -- 12.2.4.4 Expressing correlation views -- 12.2.4.5 Expressing market views - long equity -- 12.2.4.6 Expressing market views - short senior tranche -- 12.2.4.7 All-upfront basis and zero-coupon equity tranches -- 12.3 Delta hedging of synthetic CDO tranches -- 12.3.1 The principles of delta hedging -- 12.3.2 Delta hedging tranche positions with the index -- 12.3.3 Crystallising P/L from delta hedging -- 12.4 Analysis of common correlation trading strategies -- 12.4.1 Delta hedged equity tranche -- 12.4.2 Delta hedged mezz tranche -- 12.4.3 Long equity-short mezz straddle (bull-bear trade) -- 12.4.4 Equity curve flattener -- 12.5 Credit market dislocations -- 12.5.1 The May 2005 correlation 'crisis' -- 12.5.2 The credit crunch, 2007 -- 12.6 Chapter review -- 13 Risk management of a portfolio of synthetic CDOs -- 13.1 Introduction -- 13.2 Set-up of the problem -- 13.2.1 Definition of terminology -- 13.2.2 Mathematical formulation -- 13.2.3 Algorithmic implementation -- 13.3 Portfolio risk measures -- 13.3.1 Spread sensitivities -- 13.3.2 Correlation sensitivities -- 13.3.3 Concentration/overlap risk -- 13.3.4 Time decay sensitivity -- 13.3.5 Obligor default sensitivity -- 13.4 Description of the sample portfolio -- 13.5 Basic analysis of the sample portfolio -- 13.5.1 Descriptive statistics -- 13.5.2 Marginal and systemic CS01s -- 13.5.3 Portfolio spread sensitivity -- 13.5.4 Correlation sensitivity -- 13.5.5 Marginal default sensitivity -- 13.5.6 Running default sensitivity (running VoD) -- 13.5.7 Computing the worst case portfolio loss scenario -- 13.5.8 Credit spread and default VaR -- 13.6 Adding new trades to the portfolio.

13.7 Origination of synthetic CDOs.