# (p. ix) List of Figures

(p. ix) List of Figures

4.1 Optically inverted Z‐spread term structure. Ford Motor Credit, 31 December 2002. 77

4.2 Z‐spread, CDS, and BCDS term structures. Ford Motor Credit, 31 December 2002. 77

4.4 Survival probability term structures for different credit risk levels. 94

4.5 Hazard rates (forward ZZ‐spreads) for Ford and BBB Consumer Cyclicals, as of 31 December 2003. 96

4.6 Fitted par coupon for Ford and BBB Consumer Cyclicals, as of 31 December 2003. 98

4.7 Fitted Libor P‐spread for Ford and BBB Consumer Cyclicals, as of 31 December 2003. 99

4.8 CCP term structures and bond prices, Georgia Pacific, as of 31 December 2003. 100

4.13 Exponential spline factors. 118

7.3 CDX IG on‐the‐run index basis versus 5y index quote in basis points. 205

7.5 On‐the‐run ITX Tranche Quote History (0–3% maps to right axis and is % up‐front. All other tranche prices are quoted as running (p. x) spreads and map to the left axis. Since Q1 2009 the 3–6% and 6–9% have also been quoted as % up‐front with 500bp running but for the purposes of this chart they have been converted to running spreads for the entire time series). Prior to Series 9 which was effective 21 Sept. 2007 and scheduled to roll on 20 Mar. 2008 the on‐the‐run index rolled every six months, subsequently, index tranche traders have continued to quote for Series 9. 212

7.6 Base Correlation Calibration to ITX Tranches (June 2009, calibrated to data in Table 7.2). 220

7.7 Cumulative loss probability implied from ITX tranche quotes. 220

7.9 LHP cumulative loss distribution for

*P*= 10% and various correlation assumptions. 2437.10 LHP loss probability density for

*P*= 10% compared to 100 name portfolio. 2438.3 Comparison of the default distributions for the calibrated Marshall‐Olkin, Gaussian and t‐copula. 274

8.4 Tail of the portfolio default distribution for the Marshall‐Olkin, Gaussian, and t‐copula. 275

8.5 Default correlation as a function of the time horizon for the Gaussian and Marshall‐Olkin copulas. 276

8.6 Base correlation skew. 282

(p. xi) 9.6 Calibrated parameters for Diamond Default model. 302

9.10 State space of enhanced risk model. 306

9.12 Aggregated four‐state Markov chain. 310

9.14 State space of projected model. 319

9.15 (

*X*_{t},*t*) state space. 3219.16 PDP sample function. 322

10.6 The implied loss surface for iTraxx Europe 28 November 2006, where 0% <

*x*< 14% and 0 ≤*t*< 10. 374(p. xii) 10.11 The structure of the non‐zero elements in the sparse matrix

**Q**constructed in subsection 4.1.1 (see Equation (51)) with*m*= 10. 37911.2 Illustration of counterparty risk scenarios for a CDS contract. 387

11.6 As Figure 11.5 but with the hazard rates of the reference entity and counterparty swapped. 393

11.8 As previous figure but with the hazard rates of the reference entity and counterparty swapped. 394

(p. xiii) 11.12 Upper and lower bounds for the fair premium when buying protection on the [6–9%] tranche as a function of correlation with the parameters giveninthe text. 401

11.15 As Figure 11.14 but for a less risky counterparty with

*h*_{C}= 1.5%. 40414.1 Realization of

*B*_{n}, the number of exceedances in*X*_{1},*X*_{2}, …,*X*_{n}above the threshold*u*_{n}. 50914.3 Hill‐plot for the Google‐data using the POT method. 513

14.4 POT analysis of Google‐data. The negative return data (black dots) on a log‐log scale, above the threshold

*u*= 0.024. The solid line is (p. xiv) the POT fitted model to the tail. The parabolic type (dashed) curves are the profile likelihoods around VaR_{99%}and*E S*_{99%}with corresponding confidence intervals cut off at the 95% (dashed) line. 51315.4 As Figure 15.3 but for larger portfolio (100 assets). 546

15.5 Inhomogeneous portfolio (100 assets). The largest exposure is 10 × median. 546

15.8 As above but with

*β*=0.5. 55115.9 As above but with

*β*=0.7. 55115.10 As above but with

*β*=0.9. 55115.11 VaR and shortfall contributions, as % of portfolio risk, compared in a default/no‐default model. ‘A’ and ‘B’ are tail risks (large exposures to high‐grade assets) and ‘C’ is the opposite: a smallish exposure to a very low‐grade credit. In a standard deviation‐based optimization, (p. xv) C generates most risk, with A being of little importance; in a tail‐based one,Acontributes most risk. 554

16.5 CMBX—AAA. 586

16.6 CMBX—AA. 587

16.7 CMBX—A. 587

16.8 CMBX—BBB. 588

16.9 ABX—AAA. 588

16.10 ABX—A. 589

16.11 ABX—BBB. 589

17.2 Empirical versus theoretical unconditional statistics of the US HPA. 608

17.3 Cross‐correlation function between HPA and log‐payment. 611

17.4 Theflowchartofthe HPA model. 613

17.5 Composition of the 25‐MSA HPA (results of Kalman filtering, 1989–2008). 617

17.8 FHFA‐25MSA HPI forecast versus actual from 2002–end. 619

17.9 Average annualized HPI volatility. 626

17.10 Empirical unconditional volatility: indices and geography. 628

18.3 Plot of the S&P Composite‐10 Case‐Shiller Home Price Index. The peakofthe index occurredatJuly 2006. 639

18.8 Model and market quotes for the 800 calibration cusips belonging to the collateral of Biltmore CDO 2007‐1. All the ABS deals present (p. xvii) in the first collateral layer (136 deals) are calibrated and 664 of the ones in the second layer are also included in the calibration set. 648