Serge Goossens

One Factor Models for the ABS Correlation Market: Pricing TABX Tranches

In this paper we look at one factor models for TABX, the tranches of ABX.HE. Both the Gaussian copula and Levy base correlation method are applied to price the tranches. We describe adaptations made to the standard recursive approach for pricing TABX. next we compare the gaussian copula formulation with the Levy base correlation method. We show that ABX.HE and TABX reveal important information when compared to the traditional subordination levels used by the rating agencies before the credit crunch. Finally we present some results obtained with our pricing methodology and we finish by showing the necessity for market participants to be more transparent on the prepayment assumptions.

The art of credit derivatives : demystifying the black swan

About the Authors. Acknowledgements. Preface. List of Tables. List of Figures. 1 Introduction. PART I MODELING FRAMEWORK. 2 Default Models. 2.1 Introduction. 2.2 Default. 2.3 Default Models. 3 Modeling Dependence with Copulas. 3.1 Introduction. 3.2 Copula. 3.3 Using Copulas in Practice and Factor Analysis. PART II SINGLE NAME CORPORATE CREDIT DERIVATIVES. 4 Credit Default Swaps. 4.1 Introduction. 4.2 Credit Default Swap: A Description. 4.3 Modeling CDSs. 4.4 Calibrating the Survival Probability. 4.5 2008 Auction Results. 4.6 The Big Bang Protocol. 5 Pricing Credit Spread Options: A 2-factor HW-BK Algorithm. 5.1 Introduction. 5.2 The Credit Event Process. 5.3 Credit Spread Options. 5.4 Hull-White and Black-Karazinsky Models. 5.5 Results. 5.6 Conclusion. 6 Counterparty Risk and Credit Valuation Adjustment. 6.1 Introduction. 6.2 Valuation of the CVA. 6.3 Monte Carlo Simulation for CVA on CDS. 6.4 Semi-analytic Correlation Model. 6.5 Numerical Results. 6.6 CDS with Counterparty Risk. 6.7 Counterparty Risk Mitigation. 6.8 Conclusions. PART III MULTINAME CORPORATE CREDIT DERIVATIVES. 7 Collateralized Debt Obligations. 7.1 Introduction. 7.2 A Brief Overview of CDOs. 7.3 Cash versus Synthetic CDOs. 7.4 Synthetic CDOs and Leverage. 7.5 Concentration, Correlation and Diversification. 8 Standardized Credit Indices. 8.1 Introduction. 8.2 Credit Default Swap Indices. 8.3 Standardization. 8.4 iTraxx, CDX and their Tranches. 8.5 Theoretical Fair Spread of Indices. 9 Pricing Synthetic CDO Tranches. 9.1 Introduction. 9.2 Generic 1-Factor Model. 9.3 Implied Compound and Base Correlation. 10 Historical Study of Levy Base Correlation. 10.1 Introduction. 10.2 Historical Study. 10.3 Base Correlation. 10.4 Hedge Parameters. 10.5 Conclusions. 11 Base Expected Loss and Base Correlation Smile. 11.1 Introduction. 11.2 Base Correlation and Expected Loss: Intuition. 11.3 Base Correlation and Interpolation. 11.4 Base Expected Loss. 11.5 Interpolation. 11.6 Numerical Results. 11.7 Conclusions. 12 Base Correlation Mapping. 12.1 Introduction. 12.2 Correlation Mapping for Bespoke Portfolios. 12.3 Numerical Results. 12.4 Final Comments. 13 Correlation from Collateral to Tranches. 13.1 Introduction. 13.2 Generic 1-Factor Model. 13.3 Monte Carlo Simulation and Importance Sampling. 13.4 Gaussian Copula Tranche Loss Correlations. 13.5 Levy Copula Tranche Loss Correlations. 13.6 Marshall-Olkin Copula Tranche Loss Correlations. 13.7 Conclusions. 14 Cash Flow CDOs. 14.1 Introduction. 14.2 The Waterfall of a Cash Flow CDO. 14.3 BET Methodology. 14.4 Results. 14.5 AIG and BET. 14.6 Conclusions. 15 Structured Credit Products: CPPI and CPDO. 15.1 Introduction. 15.2 Multivariate VG Modeling. 15.3 Swaptions on Credit Indices. 15.4 Model Calibration. 15.5 CPPI. 15.6 CPDO. 15.7 Conclusion. PART IV ASSET BACKED SECURITIES. 16 ABCDS and PAUG. 16.1 Introduction. 16.2 ABCDSs versus Corporate CDSs. 16.3 ABCDS Pay As You Go: PAUG. 16.4 Conclusion. 17 One Credit Event Models for CDOs of ABS. 17.1 Introduction. 17.2 ABS Bond and ABCDS. 17.3 Single Name Sensitivity. 17.4 Multifactor Correlation Model. 17.5 Monte Carlo Simulation. 17.6 Results. 17.7 Conclusions. 18 More Standardized Credit Indices: ABX, TABX, CMBX, LCDX, LevX. 18.1 Introduction. 18.2 ABX and TABX. 18.3 LevX and LCDX. 18.4 CMBX and ECMBX. 18.5 Indices as Indicators. 19 1-factor Models for the ABS Correlation Market Pricing TABX Tranches. 19.1 Introduction. 19.2 Generic 1-factor Model. 19.3 Amortizing Bond and CDS. 19.4 A Simple Model for Amortization and Prepayment. 19.5 ABX.HE Credit Index. 19.6 Prepayment and Model Calibration. 19.7 Pricing Model Implications. 19.8 Conclusions. 20 Bond Price Implied Spreads. 20.1 Introduction. 20.2 Bond Price Implied Spreads. 20.3 Numerical Results. PART V DYNAMIC CREDIT PORTFOLIO MANAGEMENT. 21 Long Memory Processes and Benoit Mandelbrot. 21.1 Introduction. 21.2 Econophysics, Fat Tails and Brownian Motion. 21.3 Long-term Memory and the Nile River. 21.4 Capital Asset Pricing Model. 22 Securitization and the Credit Crunch. 22.1 Introduction. 22.2 Correlation and Mortgage-backed Securities. 22.3 Securitization and Economic Growth. 23 Dynamic Credit Portfolio Management. 23.1 Introduction. 23.2 Regulatory Capital and Basel Formulas. 23.3 Portfolio Credit Risk and Economic Capital. 23.4 Securitization and CDO Models. 23.5 CDO Pricing. 23.6 Credit Portfolio Management and Correlation Mapping. 23.7 Strategic Credit ECAP Management. 24 Conclusion. Appendix A: Economic Capital Allocation Approaches. Appendix B: Generalized Gauss Laguerre Quadrature. References. Index.

Dynamic Credit Portfolio Management: Linking Credit Risk Systems, Securitization and Standardised Credit Indices

In this paper we give a resume of the correlation concept that underlies the models for credit risk measurement, for the rating of structured products, for the pricing of (tranches of) structured products, and for Basel II capital charges. We discuss how securitization has changed the risk characteristics of the credit portfolios and enter into the requirements of transparent and liquid credit indices for the credit portfolio management and for the further development of the securitization market. To capture the evolution in the financial and economic environment (for instance, reflected in the changing risk characteristics) we formulate the basis concepts of a dynamic credit portfolio management framework, that would build further on the common static Rating Based risk methods.

One Credit Event Models for CDOs of ABS

In this paper we look at a multifactor Monte Carlo Gaussian Copula based model to price CDOs of ABSs. The probabilities of default are implied from prices of ABS bonds and several notional amortisation schedules are proposed. A detailed sensitivity analysis is done with respect to recovery rates, default intensities, amortization schedules and risky duration, for all the individual bonds. Additionally a similar analysis is done of the impact of the parameters and the amortization schedules on the prices of the different tranches of a CDO of ABSs.

Correlation Mapping Under Levy and Gaussian Base Correlation

In an earlier paper we treated the concept of Base Expected Loss (BEL) (both for the Gaussian Copula and Levy Base Correlation models) as an arbitrage free approach to interpolate the base correlation curves for pricing non-standard tranches of the standardized credit indices. In this paper we extend the approach further by using the technique to price CDOs of non-standardized portfolios (so called bespoke CDOs). That is the framework is developed in the context of correlation mapping. Additionally we compare the correlation mapping methodology developed here with alternative approaches largely used with practitioners.

Let's Jump Together - Pricing of Credit Derivatives: From Index Swaptions to CPPIs

This paper describes a dynamic multivariate jump driven model in a credit setting. We set up a dynamic Levy model, more precisely a Multivariate Variance Gamma (VG) model, for a series of correlated spreads. The parameters of the model come from a two step calibration procedure. First, a joint calibration on swaptions on the spreads is performed and second, a correlation matching procedure is applied. For the first calibration step, we make use of equity-like pricing formulas for payer and receiver swaptions, based on the characteristic function and the Fast Fourier Transform (FFT) method. In the second calibration step, we fix the correlation in the model to match the prescribed (in casu historically observed) correlation. This can be done fast since a closed form expression is readily available. The resulting jump driven dynamic model generates correlated spreads very fast. This model can be used to price a whole range of exotic structures. We illustrate this by pricing the currently popular credit Constant Proportion Portfolio Insurance (CPPI) structures. Because of the built in jump dynamics a better assessment of gap risk is possible.