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date: 21 July 2019

(p. 663) Subject Index

(p. 663) Subject Index

ABS CDOs, valuation model35, 605, 631–3, 649
and collateral structure631–2
and dual approach654–6
and historical overview of sub‐prime market633–4
and probability measure calibration642–3, 649–51
and results643
calibration and robustness643–6
CDO pricing and sensitivity analysis647–9
and scenario generator635–9
and sensitivities652–4
and severity reasoning639–42
and waterfall rules631–2
ABX series:
and concerns over management of12
and mortgage derivatives7
and sub‐prime market11
adjustable‐rate mortgages (ARMs):
and Interest‐only (IO) ARMs35
and Option ARMs35
adjusted binomial approximation246
affine jump‐diffusion (AJD) model225–6
AIG:
and AIG Financial Products14
and rescue of13–14
and risk exposure10
and super‐senior debt derivatives9
approximation of loss distribution242–8
Arrow‐Debreu theory314
asset backed securities (ABS)33–5 see also ABS CDOs
background filtration160, 161–3
Banco Comercial Portugues57
Bankers Trust3, 4
Bank for International Settlements5
and BIS Accord (2004)50
and ‘Guidance on paragraph 468 of the Framework Document’50
and warnings over growth of credit default swap sector8
Bank of England10
banks:
and risk exposure9–10
and super‐senior debt, stockpiling of9 see also parallel banking system
Barclays Capital67
base correlations218–21
Basel Capital Accord501
Basel Committee on Banking Supervision505
Basel II502
and pillar I's guidelines50
Bear Stearns11, 12
bespoke collateralized debt obligations (CDOs)221–4
Bistro (Broad Secured Trust Offering) scheme5–6
Black‐Scholes theory219, 282, 290
Black Swan488, 500
Bloomberg14
bond‐implied credit default swap (BCDS) term structure100–1
bond valuation, see credit bond valuation
bottom‐up models225–9
calibration:
and copula‐based calibration289–90
and credit triangle and default rate calibration85–8
and Marshall‐Olkin copula based models266–70
(p. 664) Calpine bonds106–7
Capital Asset Pricing Model (CAPM)225–6, 535
Case‐Shiller home price indices605, 629, 639–40
CDX (American corporate credit index)7, 18–19
central banks, and opacity of credit derivatives sector15
Chase Manhattan5
Chicago Mercantile Exchange605
Citibank57
collateralized debt obligations (CDOs)6
and attachment points18
and detachment points18
and nature of18
and pricing bespoke221–4
and pricing of278–9
and reference entity19
and structure of18
and super‐senior debt9
collateral values, and volatility of40
Commodities and Futures Exchange12
Composite Basket Model215–16
conditional independence534
constant coupon price (CCP) term structure98–100
constant maturity default swap (CMDS):
and definition of79
and pricing of190–2
constant proportion debt obligation (CPDO)214–15
consumer credit, and expansion of583–4
contagion models in credit risk285–6, 321–2
and change of measure313–14
application to point processes315–16
Piecewise‐Deterministic Markov Processes316–19
for semimartingales, Doléans‐Dade theorem314–15
and dynamic default modelling290
and filtration308–9
and general dependence concepts286–8
copula‐based calibration289–90
copulas for general joint distributions288–9
and infectious defaults model294–6
and Markov chain models300
diamond default model I300–2
diamond default model II302–3
enhanced risk model305–8, 319–21
estimation311–13
incomplete observations309–13
inhomogeneous contagion model303–5
and Markov processes296
generators and backward equations297–8
Markov chains298–300
phase‐type distributions299–300
Piecewise‐Deterministic Markov Processes309, 322–4
and network modelling approach321–2
and Piecewise‐Deterministic Markov Processes models309, 322–4
and reduced‐form model:
dual predictable projections291–2
general formulation of291
and taxonomy of modelling approaches:
factor model of rating transitions292–4
frailty models294
infectious defaults model294–6
contingency489–90
contingent claims469
and contingent claims vs projected possibility469–70
and conversion‐contingency‐price complex482
and conversion crisis482, 483–6
and differentiation by price475–7
and the exchange place479–80
and morphing of debt into equity474
and nature of484–5
and price as value of474–5
and pricing vs evaluation470–1
and reactivating conversion480–2
continuous time approximation119–21
continuous time Markov chains328–9
and change of probability measure338–41
and conditional expectations334–5
and embedded discrete‐time Markov chain333–4
(p. 665) and martingales associated with transitions337–8
and probability distribution of the absorption time336–7
and time‐homogeneous chains329–31
and time‐inhomogeneous chains331–3
convertible bonds467
and conversion from credit to equity467, 468
moment of conversion468–9
and significance of467–8
copula models215–18
and Composite Basket Model215–16
and copula‐based calibration289–90
and factor model216–17
and general joint distribution288–9
and implied copula216
and limitations of290
and Markov copulas348–51
application to ratings‐triggered step‐up bonds351–4
changes of measure351
pricing ratings triggered step‐up bonds via simulation352–4
and misuse of techniques525–8
and random factor loading model216 see also Gaussian copula model; Marshall‐Olkin copula based models
corporate bond valuation20, 66
correlation:
and diversification599–601
and structured finance instruments596–8
correlation ‘mapping’221–4
correlation skew276–7
and base correlation280–1
and compound correlation279–80
and Marshall‐Olkin skew281–2
and one‐factor Gaussian copula277–8
and pricing collateralized debt obligations278–9
counterparty risk12, 13, 207–10, 383–4, 404
and credit default swaps385
bilateral CDS counterparty risk395
buying CDS protection391–4
modelling approach388–90
parameters390–1
payoff under counterparty default386–7
quantifying credit value adjustment387–8
replacement cost391
selling CDS protection394–5
valuation with no counterparty risk385
as critical issue406
and definition of383
and modelling of29–31
and quantitative estimation of408
and structured credit products396
credit indices399
index tranches399–401
risk distribution across capital structure402–3
super‐senior risk401–2 see also credit value adjustment (CVA)
credit, and cyclical nature of17
credit bonds (CBs):
and definition of78
and pricing of82–4
credit bond valuation:
and bullet bonds:
interpolated spread (I‐spread)71
yield spread70–1
yield to maturity71
Z‐spread71–2
and callable/puttable bonds72
option‐adjusted spread 72–3
and constant coupon price term structure98–100
and continuous time approximation119–20
and credit default swap‐Bond basis107–8
CDS‐Bond complementarity109–10
coarse‐grained hedging and approximate bias114–16
consistent measures for CDS‐Bond basis113–14
static hedging of credit bonds with CDS110–13
and floating rate notes73
discount margin73–4
(p. 666) and risk‐free bonds69–70
interest rate69–70
yield to maturity70
and spread measures66–7
and strippable cash flow valuation methodology68–9
implications of risk cash flows75–8
problems with74–5
and survival‐based valuation framework78
bond‐implied credit default swap term structure100–1
bond‐specific valuation measures103–7
credit market instruments78–9
credit triangle and default rate calibration85–8
default‐adjusted spread and excess spread105–7
estimation of survival probabilities88–92
fitted price and P‐spread104–5
forward spreads and trades101–3
Fractional recovery of market value80–1
Fractional recovery of par78, 80–1
Fractional recovery of Treasury80–1
hazard rate and ZZ‐spread term structures93–6
par coupon and P‐spread term structures96–8
pricing of credit bonds82–4
pricing of credit default swap84–5
recovery assumptions in reduced‐form framework79–82
reduced form framework assumption78
survival and default probability term structures93
and Z‐spread71–2
credit default swaps (CDSs):
and changes in trading of198
and counterparty risk12, 13, 385
bilateral CDS counterparty risk395
buying CDS protection391–4
modelling approach388–90
parameters390–1
payoff under counterparty default386–7
quantifying credit value adjustment387–8
replacement cost391
selling CDS protection394–5
valuation with no counterparty risk385
and credit triangle and default rate calibration86–8
and definition of18, 78–9
and expansion of198
and hedging function8
and ‘model’ prices8–9
and moral hazard8
and opacity of sector11–12, 13
and origins of credit derivatives concept5, 18
and pricing of84–5
continuous time approximation119–21
and protection buyer18
and protection seller18
and reference entity18
and risk concentration11
and sovereign credit default swap16
and traders' pricing practices8–9
and valuation of197–8
and warnings over growth of8 see also credit default swap (CDS) market models
credit default swap (CDS)‐Bond basis107–8
and CDS‐Bond complementarity109–10
and coarse‐grained hedging and approximate bias114–16
and consistent measures for CDS‐Bond basis113–14
and static hedging of credit bonds with CDS110–13
credit default swap (CDS) market models159–60
and construction via probability ratios184–5
default swaption pricing188–9
probability ratio construction185–7
spot martingale measure and default time187–8
(p. 667) and default swaptions165
European default swaptions169–70
forward default swap spreads165–9
and detailed construction of180–3
and mathematical framework160
background filtration161–3
background processes163–5
pre‐default processes163–5
survival measures163–6
and model specification170–7
and origins of literature on159–60
and pricing of constant maturity credit default swaps190–2
and simplifications under independence of rates and credit177–80
credit derivatives:
and advantages of5
and banks' risk exposure9–10
and complexity of products8
and concerns over dismissed8
and controversy surrounding3
and counterparty risk12, 13
and credit ratings6
and criticisms of3–4, 14
and definition of196
and demand for16
and expansion of3, 6–7
and government consensus over need to change market14
and hedging function7, 8
as high profile concept4
and market reform14–15
and meaning of4
and ‘model’ prices8–9
and mortgage risk6–7
high default correlations10
and opacity of sector11–12, 13
and origins of concept3, 4–6, 18
and pricing difficulties8–9
and questions over future of15–16
and regulation of10–11, 12–13
and risk concentration10, 11
and speculation7
and sub‐prime crisis11
and super‐senior debt9
banks' risk exposure9–10
and systemic risk13
and trading and settlement processes, concern over10–11
and transparency14
credit events196
and recovery rates197
credit indices396–9
and counterparty risk399
CreditMetrics44, 257
credit rating agencies:
and credit derivatives6
and recovery ratings53–5
credit risk, and variables affecting39
credit risk models:
and application of45
and computation of matrix exponentials377–80
and credit pricing models40
first generation structural form models40–2, 290
reduced‐form models40, 43–4, 290
second generation structural form models40, 42–3
and credit value‐at‐risk (VaR) models40, 44–5
default mode models45
mark‐to‐market models45
and loss given default50–1, 56, 61
and probability density function45
and probability of default‐recovery rate relationship46–9, 60–2
and procyclicality55–6
and recovery ratings53–5 see also contagion models in credit risk;
Markov chain models
Credit Suisse3, 5, 44
credit term structures modelling66–7 see also credit bond valuation
credit triangle85
credit value adjustment (CVA):
and counterparty risk383, 384, 407
and evaluation in practice454–9
and quantifying for a credit default swap387–8
and quantitative estimation of409 see also structural default model, and credit value adjustment (CVA)
currency options484–5
(p. 668) data mining procedures in generalized Cox regressions123–4, 150
and bagging and sub‐sample aggregating136–7
and boosting generalized Cox regressions:
Friedman's gradient boosting machine134–5
using basis expansion135–6
and counting and intensity processes150–2
and Cox regression with group frailty131–3
and frailty factor for modelling dependence140
calibrate the frailty model143–5
expectation maximization algorithm140–1
Markov chain Monte Carlo methods141–3
and gamma and variance gamma processes152–5
and generalized Cox hazard models:
generalized proportional models126
partial likelihood function125–6
proportional hazard model125
and optimal choice of the parameters or Î133–4
and regularized Cox regressions:
with basis expansion128–9
elastic net and flexible penalty129–31
LARS for L1 regularized partial likelihood127–8
Ld regularization and extensions128
threshold gradient descent based forward stagewise selection131
and spline‐based strategy for credit indices:
cubic spline148
index credit swap spread145–6
piecewise constant spline147–8
spline model for default arrival intensity146–8
trading strategies for credit indices149
and stochastic covariate processes138–40
and time‐varying covariates137–8
debt472–3
and morphing into equity473–4
debt vale adjustment (DVA)395
default:
and acceleration of debt75–6
and counterparty risk modelling29–31
and credit pricing models:
first generation structural form models40–2
reduced‐form models43–4
second generation structural form models42–3
and distressed market for bonds74–5
and estimation of survival probabilities88–92
and firm‐value model20–1, 22–3
and KMV model41
and loss given default50–1
and multiple obligors24–9
and probability of default‐recovery rate relationship46–9, 60–2
and recovery ratings53–5
and reduced form model20, 21–2
default‐adjusted spread105–7
default correlation484
default probabilities, and estimation of502–3
Depository Trust and Clearing Corporation (DTCC)14
derivative payoffs469
derivative valuation theory472
Deutsche Bank6
digital default swaps (DDS):
and credit triangle and default rate calibration86–8
and definition of79
distressed bonds:
and inverted spread curve75
and market for74–5
Doléans‐Dade theorem314–15
Dutch East India Company468
enhanced risk model305–8, 319–21
Esscher tilt539–40
(p. 669) estimation:
and counterparty risk408
and Markov chain models311–13
and probability of defaults502–3
and survival probabilities88–92
European Central Bank (ECB), and report on credit derivatives sector (2009)15
exponential splines89, 118–19
exposure at default (EAD)39
Extreme Value Theory (EVT)32, 501, 531
and credit risk related issues502, 504
early warnings505
estimation of default probabilities502–3
model uncertainty504–5
portfolio models503
risk measurement503
simulation methodology503
stochastic processes504
structured products503
taking risk to extremes504
Turner Review (2009)505–7
and future developments529
and meta‐models527–8
and misuse of copula techniques525–8
and multivariate Extreme Value Theory (MEVT)503, 520–5
multivariate regular variation524
return to credit risk525–31
and one‐dimensional case507–20
estimating rare/extreme events514–15
Interludium 1517–18
Interludium 2518–20
model uncertainty513–14
remarks on516–17
and rare event simulation529–30
and risk aggregation, concentration and diversification528–9
factor model of rating transitions292–4
Fast Fourier Transform (FFT)236–7
Federal Housing Finance Agency (FHFA)605, 627–9
Feynman‐Kac formula298
financial engineering (FE)525
and limitations of528
Financial Services Authority (FSA), and regulation of credit derivatives12–13
first‐to‐default swap429–30
Fitch, and recovery ratings53
Ford Motor Co, and credit term structure76–8
forward spreads and trades101–3
Fractional recovery of market value (FRMV)80–1
Fractional recovery of par (FRP)78, 80–1
Fractional recovery of Treasury (FRT)80–1
frailty models294
Gaussian copula model19, 23–4, 213–15, 257, 288–9
and comparison with Marshall‐Olkin copula model270–1
modes of aggregate default distribution271–4
tail of the distribution274–5
time invariance275–6
and disadvantages of25–6
Gaussian distributions31, 32
Generalized Poisson Loss (GPL) model234
Girsanov theorem314
hazard rates20
and credit triangle and default rate calibration86–8
and estimation of survival probabilities88–92
and ZZ‐spread term structures93–6 see also data mining procedures in generalized Cox regressions
hedging:
and coarse‐grained hedging and approximate bias114–16
and credit derivatives7, 8
and market hedge ratio115–16
(p. 670) and static hedging of credit bonds with CDS110–13
historical data series:
and fallacy of33–4
and unreliability of583–4, 601–3
home price indices (HPI)34–5, 605
and Case‐Shiller indices605, 629, 639–40
and Chicago Mercantile Exchange Case‐Shiller futures605–6
and Federal Housing Finance Agency (FHFA) index627–9
and Home Price Appreciation (HPA) measure34, 607
jump‐diffusion pattern of607–10
oscillator property610
and Home Price Appreciation (HPA) stochastic simulator:
dataset and adjustments614
Kalman filtration615–16
model equations612–14
retrospective forecasts616–20
statistical technique614–16
and National Association of Realtors indices629
and realized vs theoretical average volatility:
conditional vs unconditional measures624–7
geographical angle627
and risk‐neutral modelling:
derivation of a risk‐neutral spot HPI process620–2
forward price623–4
mean‐reverting Markov case622–3
and RPX forwards606–7 see also ABS CDOs
home prices:
as important economic indicator604
and interest rates611–12
and modelling of34–5, 605
and price bubble604
as random processes605 see also ABS CDOs; home price indices (HPI)
homogeneous portfolios, and Markov chain models363
and calibration of366–7
and default correlations and expected default times366
and intensity specification363–4
and marginal distributions365–6
and multivariate distributions364–5
and pricing CDOs and index CDSs364
house prices, see home prices
housing market, and credit derivatives6–7 see also home prices; mortgage derivatives
incremental risk charge (IRC)502
index default swap (IDS), and pricing of203–6
index tranches396–9
and counterparty risk399–401
inhomogeneous contagion model303–5
inhomogeneous portfolios, and Markov chain models355–6
and alternative parameterizations of default intensities362–3
and calibrating via CDS spreads and correlation matrices362
and default correlations and expected default times361–2
and intensity based models reinterpreted as Markov jump processes356–7
and marginal distributions360–1
and multivariate default distributions357–60
and pricing single‐name credit default swaps362
insider trading, and crackdown on15
interest rates:
and home prices611–12
and risk‐free bonds69–70
International Swap Dealers Association (ISDA)406
and attitude towards regulation13
and auction mechanism13
and counterparty risk12
iTraxx (European corporate credit index)7, 18–19
(p. 671) J P Morgan:
and Bistro (Broad Secured Trust Offering) scheme5–6
and CreditMetrics44
and origins of credit derivatives concept3, 5, 6
and Bear Stearns12
Kamakura, and Risk Manager45
Large Homogeneous Pool (LHP) approximation242–3
LCDX (leveraged loans index)7
Lehman Brothers406
and collapse of13
and quantitative credit toolkit67
leverage, and parallel banking system584–90
Leveraged Super-Senior (LSS) trades214
loss distribution, see portfolio loss distribution
loss given default (LGD)39, 502–3
and credit risk models50–1, 56, 61
McKinsey, and CreditPortfolioView44–5
Madoff Investment Securities505
mapping methodologies221–4
market490–1
as aleatory point478
as alternative to probability487–8
and a-temporal pit of price477
and chance478–9
and contingency489–90
and contingent claims vs projected possibility469–70
and conversion-contingency-price complex482
and conversion crisis482, 483–6
and conversion from credit to equity467, 468
moment of conversion468–9
and debt472–3
morphing into equity473–4
and differentiation by price475–7
and exchange place479–80
and genesis of468, 469
and price and stochastic process471–2
and price as value of contingent claim474–5
and pricing tool486–7
and pricing vs evaluation470–1
as quantitative finance479
and reactivating conversion480–2
and suppressing possibility488–9
Markit7, 14
Markov chain models300, 327
and computation of matrix exponentials377–80
and continuous‐time Markov chains328–9
change of probability measure338–41
conditional expectations334–5
embedded discrete‐time Markov chain333–4
martingales associated with transitions337–8
probability distribution of the absorption time336–7
time‐homogeneous chains329–31
time‐inhomogeneous chains331–3
and diamond default model I300–2
and diamond default model II302–3
and enhanced risk model305–8, 319–21
and estimation311–13
and homogeneous groups model347–8
pricing348
and homogeneous portfolios363
calibration of366–7
default correlations and expected default times366
intensity specification363–4
marginal distributions365–6
multivariate distributions364–5
pricing CDOs index CDSs364
and incomplete observations309–13
and inhomogeneous contagion model303–5
and inhomogeneous portfolios355–6
(p. 672) alternative parameterizations of default intensities362–3
calibrating via CDS spreads and correlation matrices362
default correlations and expected default times361–2
intensity based models reinterpreted as Markov jump processes356–7
marginal distributions360–1
multivariate default distributions357–60
pricing single‐name credit default swaps362
and market model341–2
Markovian changes of measure343–4
model implementation344
simulation algorithm345–7
specification of credit ratings transition intensities344–5
valuation of basket credit derivatives342–3
and Markov copulas348–51
application to ratings‐triggered step‐up bonds351–4
changes of measure351
pricing ratings triggered step‐up bonds via simulation352–4
and numerical studies367–8
default correlations376–7
expected ordered default times374–6
loss distributions371–4
model calibration368–70
Markov processes28, 296
and generators and backward equations297–8
and Markov chains26–7, 141–3, 298–9
phase‐type distributions299–300
and Piecewise‐Deterministic Markov Processes309, 322–4
Marshall‐Olkin copula based models257–8, 282
and aggregate default distribution262
Duffie's approximation264–5
moment generating function262–3
Monte Carlo265–6
Panjer's recursion263–4
Poisson approximation262
and calibration of model parameters266–7
choice of common market factors267–8
inter‐sector segment267–8
intra‐sector segment267
market factor intensities269–70
parametric form of the factor loadings268–9
superior senior risk268
and comparison with Gaussian copulas270–1
modes of aggregate default distribution271–4
tail of the distribution274–5
time invariance275–6
and copula function259
equivalent fatal shock model259–60
multivariate exponential distribution260–1
and correlation skew276–7
base correlation280–1
compound correlation279–80
Marshall‐Olkin skew281–2
one‐factor Gaussian copula277–8
pricing collateralized debt obligations278–9
and model258–9
mathematical modelling:
and criticisms of506–7
and growth of19
and mistakes in533
Merrill Lynch5, 9
meta‐models527–8
model uncertainty504–5, 513
Moody's:
and CreditPortfolioManager45
and recovery ratings53
moral hazard, and credit default swap8
Morgan Stanley6
mortgage derivatives:
and development of6–7
and high default correlations10
and sub‐prime crisis11
and tradeable index7 see also ABS CDOs
(p. 673) ‘naked shorting’15
National Association of Realtors (NAR) home price indices629
network modelling321–2
Nth to default contract (NTD)206–7, 209
OAS (option‐adjusted spread)66–7, 72–3 see also Z‐spread
obligors:
and empirical analysis of19–20
and theory of individual20–3
and theory of multiple24–9
Office of the Comptroller of the Currency (OCC, USA)3, 7
parallel banking system33–4
and asset‐liability mismatch577
and birth and death of extreme leverage584–90
and collapse of structured finance bond markets583–4
and decoupling of product chain578–9
and definition of573–4
and economic impact of579–83
and fault‐line of576–7
and historical data series:
unreliability of583–4, 601–3
and role of short‐term markets577–8
and securitization574
areas covered by576
credit transformation595–6
effects of correlation596–8
synthetic securitizations574, 576
and securitization models574–6
covered bond model575
private sector model575
public sector model575
and structured finance instruments:
credit transformation595–6
effects of correlation596–8
modified rating stability view of590–3
role of rating stability in future ratings593–5
par coupon and P‐spread term structures96–8
phase‐type distributions299–300
Piecewise‐Deterministic Markov Processes (PDPs)309, 322–4
and change of measure316–19
portfolio loss distribution234–5
and approximation of loss distribution242–8, 535
accuracy and asymptocity of saddlepoint method547–8
characteristic functions535–7
computational issues549–50
conditionally independent variables548–9
CreditRisk+model535–6
direct saddlepoint approximation550–3
extended CreditRisk+ model536
inversion537–8
Merton model537
numerical examples545–7
saddlepoint approximation538–41
tail probability542–3
tranche payoffs and expected shortfall544–5
and Fast Fourier Transform236–7
and recursion237–42
price:
and conversion‐contingency‐price complex482
and differentiation475–7
and pricing tool486–7
and pricing vs evaluation470–1
and stochastic process471–2
as value of contingent claim474–5
pricing:
and credit derivatives8–9
and mathematical modelling19
probability of defaults (PD)20, 39
and credit pricing models:
first generation structural form models40–2
reduced‐form models43–4
second generation structural form models42–3
(p. 674) and credit triangle and default rate calibration85–8
and credit value‐at‐risk (VaR) models45
and estimation of502–3
and procyclicality55–6
and recovery rate39–40
relationship between46–9, 60–2
protection buyer (PB), and credit default swap18
protection seller (PS), and credit default swap18
quantitative finance, and problem classes533
Quantitative Risk Management (QRM)501, 513, 514
Radar Logic home price indices606–7, 629
Radon‐Nikodý derivatives313
random factor loading (RFL) model216
recalibration491–2
recovery rate (RR)20, 39
and credit pricing models:
first generation structural form models40–2
reduced‐form models43–4
second generation structural form models42–3
and credit value‐at‐risk (VaR) models45
and early empirical evidence56–7
and estimation of survival probabilities88–92
and examples of197
and loss given default50–1
and probability of default39–40
relationship between46–9, 60–2
and procyclicality55–6
and recent evidence57–60
and recovery ratings53–5
and stochastic recovery249–52
and traditional assumptions about39
and volatility of40
recovery swap (RS):
and credit triangle and default rate calibration86–8
and definition of79
recursion, and loss distribution237–42
reduced‐form models:
and contagion models285
and credit pricing models43–4
and dual predictable projections291–2
and general formulation of291
and single‐name credit derivatives199–203
and survival‐based valuation framework79–82
and taxonomy of modelling approaches292
factor model of rating transitions292–4
frailty models294
infectious defaults294–6
reference entity (RE):
and collateralized debt obligations19
and credit default swap18
regime‐switching model492
and calibration497
and credit default swaps:
backward equation496
definitions495–6
value in default496
and general backward equations494
coupled non‐default regimes494–5
dividends495
stand‐alone default regime494
and recalibration497–9
and regime probability493–4
and regimes492–3
and risk‐free yield curve493
regulators, and credit derivatives:
attempts to improve regulation12–13
and government consensus over need to change market14
and market reform14–15
opacity of sector11–12
trading and settlement processes10–11
unease over12
risk, and credit derivatives:
and banks' exposure9–10
and concentration of10, 11
and counterparty risk12, 13
(p. 675) and mathematical modelling19
and nature of traditional credit risk17–18
and systemic risk13
and variables affecting credit risk39
risk, and distinction from uncertainty513–14
risk concentration, and credit derivatives10, 11
risk contributions, and saddlepoint methods553–5
and shortfall560–5
conditional covariance564–5
examples565–7
first derivative560–2
second derivative562–4
and VaR contribution555–60
Risk Metrics Group44
saddlepoint methods in portfolio theory246–7, 534, 567–8
and applications of534
and approximation of loss distribution535
accuracy and asymptocity of547–8
characteristic functions535–7
computational issues549–50
conditionally independent variables548–9
CreditRisk+model535–6
direct saddlepoint approximation550–3
extended CreditRisk+ model536
inversion537–8
Merton model537
numerical examples545–7
saddlepoint approximation538–41
tail probability542–3
tranche payoffs and expected shortfall544–5
and first application of534
and risk contributions553–5
conditional covariance564–5
examples565–7
first derivative560–2
second derivative562–4
shortfall560–5
VaR contribution555–60
securitization33–5, 506
and areas covered by576
and credit transformation595–6
and diversification599–601
and effects of correlation596–8
and parallel banking system574
decoupling of product chain578–9
economic impact of579–83
fault‐line of576–7
and role of short‐term markets577–8
and securitization models574–6
covered bond model575
private sector model575
public sector model575
and synthetic securitizations574, 576
simulation methodology503
single‐ and multi‐name credit derivatives, modelling of196
and base correlations218–21
and bottom‐up models225–9
and copula models215–18
Composite Basket Model215–16
factor model216–17
implied copula216
random factor loading model216 see also Marshall‐Olkin copula based models
and correlation ‘mapping’221–4
and correlation products:
CDS contracts with counterparty risk207–10
Nth to default baskets206–7
synthetic collateralized debt obligations210–12
and Gaussian copula model213–15
and index default swap203–6
and portfolio loss distribution234–5
approximation of loss distribution242–8
Fast Fourier Transform236–7
recursion237–42
and single‐name credit default swap196
reduced‐form models199–203
and stochastic recovery249–52
and top‐down models229–34
(p. 676) single tranche collateralized debt obligations6
Sklar's theorem23–4, 288
sovereign credit default swap (CDS)16
speculation, and credit derivatives7
spread measures, and definition of66–7
Standard and Poor, and recovery ratings53
stochastic process, and price471–2
stochastic recovery249–52
strippable cash flow valuation methodology:
and credit bond valuation68–9
and implications of risky cash flows75–8
and problems with74–5
structural default model, and credit value adjustment (CVA)407, 459–60
and credit value adjustment evaluation in practice454–9
and literature overview407–8
and multi‐dimensional case416–17
and notation410–11
and one‐dimensional case:
asset value, equity and equity options413–15
asset value dynamics411
default boundary411–12
default triggering event412–13
and one‐dimensional pricing problem417–20
analytical solution432–7
asymptotic solution437–9
backward equation445–7
backward problem442–3
credit default swap435
credit default swap option435
equity put option436
fast Fourier transform method441–5
finite difference method445–8
forward equation447–8
forward problem443–4
Green's function432–3, 441–2
implementation details444–5
Monte Carlo method440–1
numerical solution439–48
survival probability433–5
and pricing problem:
Green's formula423–4
multi‐dimensional case422–3
one‐dimensional case417–20
two‐dimensional case420–2
and pricing problem for credit derivatives424
credit default swap426–7
credit default swap option428
credit default swap with counterparty risk430–2
credit value adjustment430–2
equity put option428–9
first‐to‐default swap429–30
survival probability424–6
and two‐dimensional case415–16
and two‐dimensional pricing problem420–2
analytical solution448–51
fast Fourier transform method452–3
finite difference method453–4
Monte Carlo method452
numerical solution451–4
structured credit, and counterparty risk396
and index tranches399–401
and risk distribution across capital structure402–3
and super‐senior risk401–2
structured finance instruments:
and counterparty risk396
credit indices399
index tranches399–401
risk distribution across capital structure402–3
super‐senior risk401–2
and credit transformation595–6
and effects of correlation596–8
and modified rating stability view of590–3
and role of rating stability in future ratings593–5
and unreliability of new historical data series601–3
sub‐prime crisis11, 500
and historical overview of sub‐prime market633–4 see also ABS CDOs
sub‐prime mortgage securities7
super‐senior debt9
(p. 677) and banks' risk exposure9–10
and banks' stockpiling of9
and counterparty risk401–2
survival‐based valuation framework78
and bond‐implied credit default swap term structure100–1
and bond‐specific valuation measures103–7
default‐adjusted spread and excess spread105–7
fitted price and P‐spread104–5
and constant coupon price term structure98–100
and credit default swap‐Bond basis107–8
CDS‐Bond complementarity109–10
coarse‐grained hedging and approximate bias114–16
consistent measures for CDS‐Bond basis113–14
static hedging of credit bonds with CDS110–13
and credit market instruments78–9
constant maturity default swap79
credit bonds78
credit default swap78–9
digital default swaps79
recovery swap79
and credit triangle and default rate calibration85–8
and estimation of survival probabilities88–92
and forward spread and trades101–3
and Fractional recovery of market value80–1
and Fractional recovery of par78, 80–1
and Fractional recovery of Treasury80–1
and hazard rate and ZZ‐spread term structures93–6
and par coupon and P‐spread term structures96–8
and pricing of credit bonds82–4
and pricing of credit default swap84–5
and reduced form framework78
recovery assumptions in79–82
and survival and default probability term structures93
Swiss Bank5
synthetic collateralized debt obligations6, 210–12
systemic risk500–1
top‐down models229–34
tradeable credit derivatives indices6
trading strategies for credit indices149
Treasury bonds, and common yield curves66
Turner Review (2009)505–7
UBS, and super‐senior debt9
uncertainty, and distinction from risk513–14
US Federal Reserve:
and AIG rescue13–14
and dismisses concerns over credit derivatives8
and Lehman Brothers' collapse13
and regulation of credit derivatives12–13
Value‐at‐Risk (VAR) concept:
and criticisms of505–6
and risk contributions555–60
Westpac Banking Corporation57
Z‐spread67, 71–2, 76
ZZ‐spread93–6