systemic risks; high correlation regimes; subprime crisis;

Lardy, Jean-Pierre

Patras, Frédéric

Vialard, François-Xavier

English

Research Papers in Economics

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Correlation Hypotheses, and Contagion in the Sub-
prime Crisis.
Jean-Pierre Lardy, JPLC
Fr´ ed´ eric Patras, CNRS
Zeliade Systems & CRIS.
2008 International Financial Research Forum
Paris, March 27-28•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
Based on a joint work with Franc ¸ois-Xavier Vialard, Consultant, Zeliade
Systems.
Content of the talk.
• On high regimes of default correlation.
• A simple model to take randomness of correlation and systemic risk
into account.
• Examples from the CDO and ABS market.
• Conclusion: importance of alternative methodologies for risk man-
agement.•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
Some conclusions from the subprime crisis
• Complex structured products (CDOs of ABS...) have been deviced so
as to meet rating criteria. Strong model risk (too much dependence on
the underlying models).
• Standard models failed to quantify default risk in CDOs of ABS. In
particular, AAA credit enhancements have proved entirely mispriced.
• More broadly: General failure to capture systemic contagion and high
default correlations regimes (credit quality of borrowers, monoline
insurers, housing market, liquidity crunch...).•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
Our purpose today:
• Focus on certain shortcomings of standard pricing methods for structured
ﬁnance and credit risk assessment.
• Favorite example: CDO tranches, but conclusions hold for any credit port-
folio/ structured product.
• Concentrate on senior tranches which price reﬂects extreme risks (systemic
and macroeconomic risks, liquidity, funding and counterparty risk, some
operational risk...)•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
On Gaussian assumptions
• Recall brieﬂy the standard methodology for large portfolios credit risk as-
sessment (Bank exposures in Basel 2 in the advanced IRB approach, in-
cluding retail investment; CDO tranches on CDS...):
• In the basic one-factor Gaussian copula model, the default of the i-th issuer
is triggered by the value of a Gaussian variable:
Gi = ρV +
p
1 − ρ2Vi
where ρ stands for the correlation of Gi to a market-wide random variable
V .•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
On Gaussian assumptions (2)
• Shortcomings of the model are well-known for CDO tranches: different
levels of correlation are associated to the various tranches (implied base
correlation curves).
• Stochastic correlation or Random factor loadings (RFL) models did im-
prove the picture (both theoretically and quantitatively):
Xi = ρ(V )V + γVi − m
with (V,V1,...,Vn) independent normal Gaussian variables, and ρ(V ) =
α1V ≤θ + β1V >θ.
• Here, α > β stand for two correlation regimes (high, bearish, resp. low,
bullish, since default correlation tends to increase when the economy dete-
riorates). The parameters m and γ are chosen so that Xi has mean 0 and
variance 1 (thus m is the mean of ρ(V )V ).•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
On RFL shortcomings
• But: random levels of correlation still fail to account for the price of senior
tranches !
• Reason: Gaussian copula models, however sophisticated, fail to modelize
correctly tails of portfolios loss distributions.
• Our conclusion is that a three parameters model ﬁts market prices of
tranches and gives a sound appreciation of risks: we add to the RFL model
a systemic default intensity λ.
• The parameter measures roughly the spread of the most senior tranches of
the structure and accounts for the risk premia (over the risk free interest
rate) of these tranches. In particular it accounts, besides systemic risk, for
risks that are mispriced in standard copula/credit risk models such as liq-
uidity risk or counterparty risk.•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
A closed formula for the expected loss of the (A,B) tranche at ma-
turity t in the large pool approximation (requiring only Normal and Bivariate
Normal cumulative distributions):
EL(A,B)(t) = (1 − exp(−λt))(B − A) + exp(−λt) × RFL term
where:
RFL term = EL
cond
(A,1)(t) − EL
cond
(B,1)(t),
EL
cond
(A,1)(t) = (1 − R)[Φ2(θ1,
C(t) + m
√
γ2 + α2,
α
√
γ2 + α2) −
A
1 − R
Φ(θ1)] + (1 − R)[Φ2(θ2,
C(t) + m
√
γ2 + β2,
β
√
γ2 + β2) − Φ2(θ,
C(t) + m
√
γ2 + β2,
β
√
γ2 + β2)
−
A
1 − R
(Φ(θ2) − Φ(θ))]}
with θ1 = min(θ,
m+C(t)−γΦ−1(A/(1−R))
α ), θ2 = max(θ,
m+C(t)−γΦ−1(A/(1−R))
β ),
and where C(t) is a default threshold calibrated on CDS spreads.•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
Zeliade Systems had been advocating this ERFL
model since early 2006
The ERFL (enhanced random factor loadings) model combines the advantages
of:
• Random Factor Loadings originally proposed by Andersen & Sidenius
(2005)
• Gaussian one-factor associated with a systemic default spread model origi-
nally proposed by Minh, Thompson, Devarajan (2005)
Its parameters have a clear practitioners interpretation:
• Correlation is notoriously prone to successive regimes
• The stress regime can be interpreted as the worst year of a credit cycle
• Composite multi-name credit spreads including a systemic default risk
Implementation is easy thanks to a closed-form solution in the ”large pool”
approximation. Efﬁcient saddle-point implementation for granular portfolios
allows to price 100+ names portfolios with time bucketed Greeks in a few sec-
onds.•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
Calibration of the European investment grade index (September 2007)
European Investment Grade Credit Derivatives Index (iTraxx)
Table 1 Portfolio Large Pool Model Proxy
21/09/2007 Model EGC ERFL RFL Base Cor. rating
ITX 5 Year Alpha2 13.9% 18.1% 31.1%
Index 36bp Beta2 11.4% 8.0%
RR 40% Theta -2.2 -2.2
SDIa 20.0 14.0
Tranches Mkt Price Model Prices
0-3 (upfront) 18.7% 15.1% 19.5% 28.2% 28.6% NR
3-6 (bp) 86.7 88.6 86.8 87.2 41.7% BBB
6-9 (bp) 36.1 30.1 36.1 30.9 50.8% AA
9-12 (bp) 23.2 21.7 23.2 29.7 57.6% AAA
12-22 (bp) 14.3 20.0 15.1 16.3 73.3% AAA
RFL and GC models do not satisfactorily calibrate both the Equity, Mezzanine and Senior tranches
and explain the steep base correlation skew:
• RFL overprices (resp. GC underprices) equity risk and both do not discriminate senior and
senior mezzanine
Market prices imply 3 regimes of correlations:
• Low correlation (beta=11.4%) with infrequent (theta=-2.2) higher correlation (alpha=18.1%)
regimes
• Systemic default can be considered as 100% correlation
Systemic default intensity corresponds to 23% of index spread (SDI= 0.14% and RR=40%)
aSDI: systematic default intensity•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
Calibration of the European investment grade index (March 2008)
European Investment Grade Credit Derivatives Index (iTraxx)
Table 1 bis Portfolio Large Pool Model Proxy
03/06/2008 Model EGC ERFL RFL Base Cor. rating
ITX 5 Year Alpha2 31.8% 27.7% 77.8%
Index 126bp Beta2 11.9% 4.5%
RR 40% Theta -1.2 -1.3
SDIa 120.1 91.8
Tranches Mkt Price Model Prices
0-3 (upfront) 42.5% 30.5% 48.8% 59.5% 47.5% NR
3-6 (bp) 510 525.7 515.9 526.2 59.4% BBB
6-9 (bp) 321.5 304.8 319.8 264.7 66.1% AA
9-12 (bp) 231.5 212.1 232.0 232.1 71.1% AAA
12-22 (bp) 126.5 151.5 132.2 217.2 84.5% AAA
RFL overprices (resp. ECG underprices) equity risk and both poorly discrimate senior and senior
mezzanine
Market implied regimes of correlations:
• Low correlation (beta=11.9%) with now more frequent (theta=-1.2) high correlation (al-
pha=27.7%) regime
• Systemic default intensity corresponds to 43% of index spread (SDI= 0.92% and RR=40%)
aSDI: systematic default intensity•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
Calibration of a generic European RMBS deal based on primary market
statistics in the years 2004–2006
European Prime Residential Mortgage Securitization (RMBS)
Table 2 Portfolio Large Pool Model Proxy
Prime RM Model EGC ERFL RFL Base Cor. rating
WAL 5 Year Alpha2 4.2% 8.4% 85.3%
NIM 25bp Beta2 0.1% 1.5%
RR 60% Theta -1.93 -2.13
SDI 30.7 27.9
Tranchesa Mkt Price Model Prices
0-1% (upfront) 40% 37.6% 41.7% 53.5% 25.0% NR
1-2.5% (bp) 80 81.5 79.8 92.0 49.3% BBB
2.5-4% (bp) 40 31.1 40.3 38.9 61.0% A
4-6% (bp) 25 30.7 28.8 38.7 70.9% AA
6-100% (bp) 12 11 10 6.9 N/A% AAA
Necessity of the 3 regimes:
• ”Independence” (beta=0.1% compared to 11.4%) in the low correlation regime
• Lower correlation (alpha= 8.4% compared to 18.4%) in the stress regime
• Higher inﬂuence of the systemic risk, corresponding to 45% of the pool’s spread
EGC and RFL model have poor calibration and discrimination of A and AA tranches.
aAttachment points include beneﬁt of 0.4% reserve account from excess spread•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
Calibration of a generic European SME deal based on primary market
statistics in the years 2000–2006
European SME loans securitization
Table 3 Portfolio Large Pool Model Proxy
SME Model EGC ERFL RFL Base Cor. rating
WAL 4 Year Alpha2 7.1% 8.0% 59.0%
NIM 75bp Beta2 0.1% 5.0%
RR 50% Theta -1.8 -2.06
SDI 46.1 38.2
Tranchesa Mkt Price Model Prices
0-4% (upfront) 35% 32.2% 35.2% 40.2% 23.5% NR
4-6% (bp) 120 122.1 120.8 120.4 34.1% BBB
6-8% (bp) 65 57.4 65.1 54.8 42.5% A
8-11% (bp) 40 47.4 41.9 53.0 52.4% AA
11-100% (bp) 18 20.1 16.7 10.7 N/A AAA
Necessity of the 3 regimes:
• Correlation regimes close to the RMBS calibration
• Systemic risk inﬂuence similar to the IG index (25% of composite spread)
aAttachment points include beneﬁt of 1.4% reserve account from excess spread•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
ERFL model parameters interpretation is valuable in a broader universe
of ABS and multi-name credit assets
Based on pre-crisis market levels calibrations, ERFL parameters are more in-
formative than base correlation:
• Theysuggestseriousshortcomingsofclassicalcorrelationneutralstrategies
• Super senior risks captured by composite spread instead of correlations
Across credit asset classes:
• Corporate credit risk has a higher correlation than SME or Retail credit in
normal and stress regime (as could be expected)
• Residential mortgage credit has a higher proportion of systemic risk in the
composite spread:
– Importance of the real estate markets
– Leverage of households
– Banks concentration in the segment
– Jobs & real economy•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
With hindsight, the current ”sub-prime” crisis provides clear elements in
its favour:
AAA and super senior risks are better captured by composite spread
• Fear contagion, liquidity squeeze, loss of conﬁdence in origination stan-
dards or rating methodologies happen with 100% correlation (!)
Structured credit disasters such as CDOs of HEL mezzanine ABS could have
been avoided
• Much higher AAA CDO-square credit enhancement from the high propor-
tion of SDI in the composite spread
• More scrutiny would have resulted on BBB pieces of HEL ABS
Composite spread concept is equally useful for counterparty credit risk on credit
derivatives or monoline credit enhancement•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
INTRODUCING THE CRIS PLATFORM
The future
...will require rebuilding of conﬁdence
...reporting and disclosure will identify the winners and losers, and emphasize
the long term value of risk management
...markets and regulations will require more transparency on risk and models
...requires a data, model, valuation and risk management portal whose commer-
cial success can be ”public good” for the industry
Zeliade Systems, OTC-Conseil and JPLC, together with Dexia CLF, Mi-
crosoft France and the University of Evry are partners of such a project,
called ”CRIS” recently selected by the Pˆ ole de competitivit´ e Finance In-
novation. The project was chosen at the 5th “appel d’offre FUI”.•First •Prev •Next •Last •Go Back •Full Screen •Close •Quit
References:
• L. Andersen and J. Sidenius, Extensions to the Gaussian Copula: Random
Recovery and Random Factor Loadings, Journal of Credit Risk, 2005
• T. Bielecki and M. Rutkowski, Credit Risk: Modeling, Valuation and Hedg-
ing, Springer-Verlag, Berlin, 2002.
• J-P. Lardy, F. Patras, F.X. Vialard, CDOs: how far should we depart from
Gaussian copulas?, Zeliade Systems, December 2007 (to be published)
• Ph. Schonbucher, Credit Derivatives Pricing Models, Wiley 2003
• M. Trinh, R. Thompson and M. Devarajan, Relative Value in CDO
Tranches: A View through ASTERION, QRC Quarterly, Q1 2005.

CDOs: how far should we depart from Gaussian copulas?, Zeliade Systems,

Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings,

Correlation, CDOs of ABS and the subprime crisis.

http://basepub.dauphine.fr/xmlui/bitstream/123456789/7112/1/s15_lardy-slides.pdf

Correlation, CDOs of ABS and the subprime crisis.

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