Garcia goossens the art of credit derivatives; demystifying the black swan (2010)

Table of Contents Title Page Copyright Page About the Authors Acknowledgements Preface List of Tables Table of Figures Chapter - Introduction Part I - Modeling Framework Chapter - Default Models 2.1 INTRODUCTION 2.2 DEFAULT 2.3 DEFAULT MODELS Chapter - 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 Chapter - 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 Chapter - 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 Chapter - 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 Chapter - 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 Chapter - 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 Chapter - Pricing Synthetic CDO Tranches 9.1 INTRODUCTION 9.2 GENERIC 1-FACTOR MODEL 9.3 IMPLIED COMPOUND AND BASE CORRELATION Chapter 10 - Historical Study of Lévy Base Correlation 10.1 INTRODUCTION 10.2 HISTORICAL STUDY 10.3 BASE CORRELATION 10.4 HEDGE PARAMETERS 10.5 CONCLUSIONS Chapter 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 Chapter 12 - Base Correlation Mapping 12.1 INTRODUCTION 12.2 CORRELATION MAPPING FOR BESPOKE PORTFOLIOS 12.3 NUMERICAL RESULTS 12.4 FINAL COMMENTS Chapter 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 LÉVY COPULA TRANCHE LOSS CORRELATIONS 13.6 MARSHALL-OLKIN COPULA TRANCHE LOSS CORRELATIONS 13.7 CONCLUSIONS Chapter 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 Chapter 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 Chapter 16 - ABCDS and PAUG 16.1 INTRODUCTION 16.2 ABCDSS VERSUS CORPORATE CDSS 16.3 ABCDS PAY AS YOU GO: PAUG 16.4 CONCLUSION Chapter 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 Chapter 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 Chapter 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 Chapter 20 - Bond Price Implied Spreads 20.1 INTRODUCTION 20.2 BOND PRICE IMPLIED SPREADS 20.3 NUMERICAL RESULTS Part V - Dynamic Credit Portfolio Management Chapter 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 Chapter 22 - Securitization and the Credit Crunch 22.1 INTRODUCTION 22.2 CORRELATION AND MORTGAGE-BACKED SECURITIES 22.3 SECURITIZATION AND ECONOMIC GROWTH Chapter 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 Appendix A - Economic Capital Allocation Approaches Appendix B - Generalized Gauss Laguerre Quadrature References Index Table of Figures Figure 3.1 Generating default times using a Gaussian copula Figure 6.1 Counterparty default index Figure 7.1 Typical CDO structure Figure 8.1 Standardized credit indices corporates: iTraxx and CDX and the tranches Figure 9.1 Implied compound correlation Figure 9.2 Gaussian copula base correlation Figure 9.3 Compound correlation can hit 0% for mezzanine tranches Figure 9.4 Base correlation can hit 100% for senior tranches Figure 9.5 Gaussian BC curves recovery rates Figure 9.6 Lévy BC curves recovery rates Figure 10.1 iTraxx Europe Main on-the-run 5-year spreads Figure 10.2 iTraxx Europe Main 5y Gaussian and Lévy Base Correlation for 12-22 tranche Figure 10.3 Gaussian copula base correlation Figure 10.4 Lévy base correlation Figure 10.5 iTraxx Europe Main 5-year delta for 0-3 tranche Gaussian and Lévy model Figure 11.1 Base correlation concept Figure 11.2 Gaussian copula base correlation history Figure 11.3 Distribution of the expected loss over the tranches as a percentage of the total expected loss (5-year iTraxx) Figure 11.4 Construction of the bounds on the base expected loss on April 2008 Figure 11.5 Gaussian copula base expected loss The dash/dotted lines show the upper and lower bounds The solid line shows the monotonic cubic spline interpolation and the dashed line shows the shape preserving cubic interpolation Figure 11.6 Lévy base expected loss The dash/dotted lines show the upper and lower bounds The solid line shows the monotonic cubic spline interpolation and the dashed line shows the shape preserving cubic interpolation Figure 11.7 Gaussian copula base correlation The dash/dotted lines show curves implied from the upper and lower sounds on base expected loss The solid lines show the curve for monotonic cubic spline interpolation and the dashed line shows the shape preserving cubic interpolation Figure 11.8 Lévy base correlation The dash/dotted lines show curves implied from the upper and lower bounds on base expected loss The solid line shows the curve for monotonic cubic spline interpolation and the dashed line shows the shape preserving cubic interpolation Figure 11.9 Gaussian copula base correlation on April 2008 The dash/dotted lines show curves implied from the upper and lower bounds on base expected loss The solid line shows the curve for monotonic cubic spline interpolation Figure 11.10 Lévy base correlation on April 2008 The dash/dotted lines show curves implied from the upper and lower bounds on base expected loss The solid line shows the curve for monotonic cubic spline interpolation Figure 12.1 Correlation mapping and the pricing of bespoke portfolios concepts correlation mapping definition historical study tranche loss correlations Gaussian framework for pricing GDP statistics generalized Gauss-Laguerre quadrature geometric Brownian motion Germany global correlation (G-Cor), concepts Goldman Sachs Gordy, M government sponsored enterprises (GSEs) Greece Greenspan, Alan GSEs see government sponsored enterprises hazard-rate models see intensity models heavy tails hedging HiVol iTraxx index see also iTraxx housing bubbles HSBC Hull and White model (HW) Hurst, Harold HW see Hull and White model HYindex hybrid CDOs, definition IC see interest coverage tests ICC see implied compound correlation Icelandic banks idiosyncratic risk, concepts implied compound correlation (ICC) concepts critique definition implied volatility see also volatility options importance sampling, concepts index reference inflation innovations insurance contracts see also credit default swaps concepts intensity models see also Cox processes; reduced-form models Black-Karazinsky model concepts definition interest rate modelling trees interest coverage tests (IC) interest rate modelling Hull and White model intensity models Ornstein-Uhlenbeck process trees interest shortfalls, PAUG intermediation business cases internal rating based framework (IRB), concepts International Swap Derivatives Association (ISDA) Internet bubble interpolation issues alternative approaches base correlation concepts cubic spline interpolation intuition, base correlation IRB see internal rating based framework ISDA see International Swap Derivatives Association iTraxx see also credit indices CDX contrasts concepts tranches types Japan John Conway’s Game of Life joint defaults, counterparty risk joint loss distributions, computations JP Morgan jump processes see alsoévy ; Poisson kurtosis lambda latent variable models, concepts LBO market LCDSs see also credit default swaps; concepts LCDX see also loans concepts definition legal contractual obligations Lehman Brothers leverage leveraged super seniors (LSSs), concepts LevX see also loans concepts Lévy processes see also base correlation; jump processes; Poisson concepts CPPIs/CPDOs LGD see loss given default LIBOR linear amortization profile linear correlation, concepts Lintner, John liquidity problems see also mark to market loans see also; LevX long positions long-term memory processes concepts Nile river study loss distributions, computations loss given default (LGD) concepts definition LSSs see leveraged super seniors Macaulay duration Mainindex see also Main iTraxx index see also iTraxx Mandelbrot, Benoit see alsoévy processes marginal distributions of default times mark to market approaches, concepts market invariants, concepts market value CDOs, definition Markit Markowitz, H Marshall-Olkin copula, tranche loss correlations martingales maturities base correlation extensions standardized credit indices MBSs see mortgage-backed securities MC see Monte Carlo simulation mean reversion Merrill Lynch Merton model Mexico mezzanine tranches mitigation approaches to counterparty risk MMR see modified modified restructuring model risks, CPPIs/CPDOs models, concepts modern portfolio theory (MPT), concepts modified modified restructuring (MMR), concepts modified restructuring (MR), concepts moneyness-at-maturity correlation mapping approach monotonicity filters Monte Carlo simulation (MC) ABS collateral correlations CDOs of ABSs concepts CPPIs/CPDOs CVA on CDSs Moody’s Moody’s KMV model Morgan Stanley mortgage-backed securities (MBSs) mortgages Mossin, Jan MR see modified restructuring multifractal models, volatility multiname credit derivative instruments see also collateralized debt obligations; first concepts types multivariate variance gamma processes (MVG) calibration issues concepts negative convexity effects of tranching net asset values (NAVs) neutral economic activity Newton-Raphson iteration, concepts Nietzsche, Friedrich Nile river study, long-term memory processes Nissan Motor Manufacturing Ltd no-arbitrage arguments no-mapping correlation mapping approach non-knockout index options, concepts normal cumulative distribution function see also Gaussian numerical integrationévy base correlation, concepts obligators, default concepts OC see overcollateralization off-balance sheet instruments see also securitization oil shocks of the one-factor Gaussian copula model see also copulas concepts definition one-factorévy model see alsoévy processes concepts optimization calibration method, survival probabilities options see also credit spread ; swaptions Black and Scholes formula concepts implied volatility Ornstein-Uhlenbeck process OTC see over-the-counter OTM see out-of-the-money options out-of-the-money options (OTM) over-the-counter (OTC) overcollateralization (OC) overview of the book P&L see profit and loss Pareto analysis, returns pay as you go features (PAUG) see also ABCDSs concepts dealer templates definition end-user templates PCA see principal component analysis Pearson correlation coefficient pension funds performance issues, copulas point processes Poisson processes see also counting ; Cox ; jump ;évy CDSs concepts portfolio dependency issues, dynamic credit portfolio management framework portfolio management power laws, concepts prepayment assumptions, mortgage pools present values price discovery, concepts price implied basis PricewaterhouseCoopers pricing ABSs art/science aspects base correlation CDOs CDOs of ABSs CDSs concepts CPDOs CPPIs credit derivative concepts CSOs Gaussian framework for pricing recovery rates standardized credit indices swaptions synthetic CDOs tranches principal component analysis (PCA) concepts definition probability-matching correlation mapping approach profit and loss (P&L) put options see also options quadratic amortization profile queuing processes random numbers rank correlation, concepts rating change momentum, concepts ratings based approach (RBA) see also credit ratings concepts RCAP see regulatory capital RCF see risky counterparty fee RD see risk duration real estate rebalancing frequencies recessions recovery rates cash CDOs CDOs of ABSs CDSs credit crunch CVA pricing statistics recursion algorithm, concepts reduced-form models see also intensity models concepts reference names credit derivatives returns references regression coefficients, Lévy/Gaussian deltas regulatory capital (RCAP) see also economic capital relative losses, definition remittance reports, prepayment assumptions rho risk duration (RD) risk management risk weighted assets (RWAs), concepts risk-factor models risk-free annuities risk-free interest rates risk-neutral measures, concepts Riskin, Shlomo risky counterparty fee (RCF) rollover mechanisms, standardized credit indices Rousseau, Jean-Jacques Royal Bank of Scotland (RBS) RR see recovery rates Russia RWAs see risk weighted assets saddle point approximations Saint-Exupery, Antoine de sandpile problems Sartre, Jean-Paul scenario analysis Schiller, Robert Schopenhauer, Arthur Schultz, Charles M SEC securitization business model of financial institutions concepts correlations credit crunch definition economic importance housing bubbles lessons learned solution to the problems statistics systemic risk uses self-organized criticality (SOC), concepts self-similarity, volatility outbursts sellers of CDSs see also counterparty risk; float payers concepts semi-analytic correlation model, concepts senior debt sensitivity analysis Shanghai Stock Exchange shareholders Sharpe, William Shaw, Bernard shifted Gamma distributions, concepts short positions buyers of CDSs Simpson’s rule single name credit derivative instruments see also credit default swaps concepts single name sensitivity, CDOs of ABSs smiles base correlation volatility smiles SOC see self-organized criticality Société Générale Spearman’s rank correlation special purpose vehicles (SPVs) see also collateralized debt obligations concepts definition spreads, standardized credit indices Standard & Poor’s Rating Services (S&P) standard errors standardized credit indices see also ABX ;; CMBX; iTraxx;; LevX; systemic risk; TABX Chinese Correction (Black Tuesday In China) concepts elements expected loss indicator uses legal issues mark to market value maturities pricing strikes theoretical fair spreads uses static reference portfolios, standardized credit indices step-up features, PAUG stochastic calculus stochastic processes, concepts strategic credit ECAP management see also economic capital stress tests strikes, credit indices structured credit products see also constant proportion concepts definition structured finance CDOs see also asset backed securities; mortgage-backed securities student loans subadditive risk measures subordinated obligations subprime MBSs see also ABX survival probabilities calibration issues concepts discount factors swaps see also first to default baskets swaptions concepts credit indices pricing syndicated loans see also CLOs Syndicated Secured Loan List synthetic CDOs concepts critique definition leverage issues pricing synthetic instruments advantages definition systemic risk see also standardized credit indices collateral concepts securitization VIX index TABX.HE see also credit indices; tranches concepts definition important points pricing uses tail dependencies concepts uses tails, heavy tails taxes, CDOs Templeton, John theoretical fair spreads, credit indices time varying assumptions, dynamic credit portfolio management framework TLCDX TMT traffic lights tranches see also ABCDSs; collateralized debt obligations; TABX ABS collateral correlations cash flow CDOs CDX concepts definition deltas iTraxx negative convexity effects pricing transparency issues Treynor, Jack trinomial trees true CDS value, counterparty risk true sales, CDO concepts trustees, CDOs Turov, Daniel Twain, Mark two-factor HW-BK algorithm UBS upfront fees, CVA US Value-at-Risk (VaR) variance gamma processes (VG) calibration issues concepts parameters Vasicek, O VG see variance gamma processes VIX index, systemic risk volatility clustering tendencies critique implied volatility multifractal models self-similarity of outburst volatility smiles see also implied volatility WAC see weighted average coupon WAFICO see weighted average FICO score WAL see weighted average life WAR see weighted average recovery rate WARF see weighted average rating factor waterfalls (indenture), cash flow CDOs weighted average coupon (WAC) weighted average FICO score (WAFICO) weighted average life (WAL) weighted average rating factor (WARF) weighted average recovery rate (WAR) weights, computation algorithms writedowns, credit events XOver spreads yield curves Zeebrugge zero coupon bonds Index compiled by Terry Halliday (HallidayTerence @ aol com) The [0-3%] equity tranche is quoted as an upfront payment plus 500 basis points (a basis point is equal to 0.01%) running http://www.zerotohundred.com/2009/auto-news/problems-at-nissan-test-track-used-as-parking-lotfor-unsold-cars As measured by the total cVaR that takes into account the whole correlation structure of the portfolio ... 2007 The quotes at the begining of each chapter have been selected to honour their work Nowadays, the metaphor of the black swan is sometimes used to describe the credit crunch It is the fruit of. .. used for the evaluation of those instruments The increased level of sophistication of the credit instruments, as evidenced by the credit crunch of June 2007, brought up the necessity for credit. .. of the CDO structure Table 14.3 Fees to be paid during the lifetime of the CDO Table 14.4 Hedge fees to be paid during the lifetime of the CDO All the contracts are payers The instrument in the