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CDO
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Collateralized Debt Obligations
Autumn School on Risk ManagementOctober 02, 2003
Modeling and Evaluation
Christian BluhmGroup Credit Portfolio ManagementGCP3 - Structured Finance AnalyticsHypoVereinsbank
Sederanger 5D-80538 Munich, Germanyphone 089-378/46033email [email protected]
This talk reflects the opinion of the author and not the opinion of HypoVereinsbank.
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 2
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Agenda
• CDOs: Motivations, Structures, and Trends
• The Mathematics of CDOs
• Some Examples and Applications
• Concluding Remarks
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CDOs: Motivation, Structures, and Trends
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 4
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What is a CDO? An Abstract View ...
credit riskyinstruments:• bonds• loans• CDS• ABS ...
tranchedsecurities:• senior classes• mezzanines• junior classes• swaps
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 5
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Motivation I: Arbitrage Opportunities
SuperSenior Investor
Class A Note Investor
Class B Note Investor
Class C Note Investor
Class D Note Investor
ARTEMUS
CreditProtectionPayments
CDSPremium
Collateral Assets & EligibleInvestments
P & IInvestments
Redemptionto makeCreditProtectionPayments
Credit DefaultSwaps
Bonds, Loans, ABS
Credit Portfolio
P & I
HedgeCounterparties
Hedgepayments
P & IInvestments
UNFUNDED
FUNDED
Subord. Note Investor
ARTEMUS Strategic Asian Credit Fund (HVB Asset Management Asia)
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 6
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Motivation II: Regulatory Capital Relief
Cash-Collateral for Classes A,B, C and D
(Held by A1+/F1+-rated bank)
ReferencePortfolio
HVB
Class A Notes(AAA)
Class B Notes(AA)
Class C Notes(A)
Class D Notes(BBB)
OECD-Bank/sCredit Default Swap
( A+)
Fixed RatePayment
Credit Linked Notes
Reimbursement of Realised Losses
Interest Sub participation,Reimbursement of Realised Losses
Class E Swap(priv. rated)
Use of proceeds
BUILDING COMFORT 2002 (HVB AG)
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 7
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Motivation III: Funding (True Sales)
• Instead of synthetic transfer by means of derivative constructions, assets are „physically“
transferred/sold (off-balance sheet) to an SPV/Issuer („true-sale“ transaction).
• Main advantage for the originating bank is funding: the notional amount (sometimes net
of a discount/loss reserve) of the asset pool is paid as cash to the asset seller/originator.
• Funding by securitizations is an efficient tool to reduce funding costs, because ratings
of true-sale CDO tranches are no longer linked to the rating of the originator after selling
the assets. However, if the originator continues the servicing/administration of the loan
pool, some seller/servicer risk remains.
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 8
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Motivation IV: Economic Risk Transfer
before Sec.after Sec.
LOSS
FREQ
UEN
CY
retained risk transferred risk / capped losses
- illustrative -
before Sec.after Sec.
EXPECTED LOSS
EXPE
CTE
D G
RO
SS M
AR
GIN
30% EL reduction
15% margin drop(structural costs)
• improvement of risk/return
• efficient cap on tail event losses
• turn-down of internal risk costs (insurance paradigm)
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 9
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Trends and Expectations
• issuance is likely to increase again (2003 was and still is a difficult year ...)
• Germany: true sale initiative; GB/USA: more synthetics
• structures become more complex, e.g.,
• structured products as underlyings (CDOs of ABS, CDOs of baskets, etc.)
• hybrid structures
• mark-to-market trigger
• issuers already think towards the Basel II securitization framework
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The Mathematics of CDOs
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 11
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Basic Ingredients
• portfolio model reflecting the risk/return of underlying assets
• cash flow model reflecting the structural definitions of the transaction
credit riskyinstruments:• bonds• loans• CDS• ABS ...
credit riskyinstruments:• bonds• loans• CDS• ABS ...
tranchedsecurities:• senior classes• mezzanines• junior classes• swaps
tranchedsecurities:• senior classes• mezzanines• junior classes• swaps
,(Ω
• simulation of an asset scenario
• application of X results in a cash
flow scenario on the liability side
• repeat this many times
• obtain distribution of tranche‘s
losses, IRR‘s, hitting probabilities,
net present values, etc.
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 12
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Choice of Portfolio Model
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 13
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Default Times from Credit Curves
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 14
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Credit Curves from S&P Data
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
1 21 41 61 81 101 121 141 161 181
AAAAAABBBBBBCCC
time (in quarters)
probability
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 15
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• good ratings can be expected to
default later in time
• bad ratings can be expected to
default in the near future
• we calibrated our credit curves
only up to a 50-year horizon
• shortest considered period
is a quarter of a year
Default Times Distributions
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
2.00%
1 21 41 61 81 101 121 141 161 181
AAAAAABBBBBBCCC
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 16
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Multivariate Default Times Distribution
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 17
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Choice of Copula: CDO Implications
Gauss copula (df=\infty) normal marg. t-copula (df=3) normal marg.
df: \infty ® 3
Different copulas impact different tranches differently. For example, moving from a Gaussianto a t-copula with degrees of freedom, say, lower than 10 will heavily stress senior tranches.
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 18
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cash flow profile of a bond (fixed coupon):
timesemiannually
Ratingτ
cash flow profile of the bond w.r.t. default timing:
timesemiannually
recovery
Example: Cash Flow Transformation
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 19
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A Random Walk Through SomeExamples and Applications
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 21
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Example: Excess Spread ModelingE
xces
s S
prea
d
Loss on Funded Part
• same amount of loss on funded volume
combines with completely different excess
spread scenarios
• timing of defaults determines overall level
of collected excess spread
• various applications in transactions
• protection mechanisms
• portfolio engineering, ...
- illustrative -
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 22
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Basic MCS Output: EDF and EL of Tranches
STD Equity Class C Class B Class A Super SeniorVol. [USD] 36,000,000 16,000,000 18,000,000 30,000,000 700,000,000Vol. [%] 4.50% 2.00% 2.25% 3.75% 87.5%Rating NR BBB A AA AAAMaturity Sep 2008 Sep 2008 Sep 2008 Sep 2008 Sep 2008Spreads N/A 3.50% 1.20% 0.40% 0.15%EDF (cumul.) 58.51% 6.27% 2.19% 1.11% 0.25%EL (cumul.) [%] 25.54% 4.23% 1.68% 0.55% 0.01%EL (cumul.) EUR] 9,194,900 676,390 302,080 163,850 55,890LGD 43.66% 67.47% 76.49% 49.12% 3.19%
• CDS of 80 traded European names; good industry mix
• average rating BBB+ (20bps average PD), 34% recovery expected
• plain vanilla structuring:
• good cash flows (interest, amortization) top-down allocation
• bad cash flows (losses) bottom-up allocation
• 5 year bullet (swap/protection) profiles, no management/replenishment (static pool)
• average level of asset correlation in the CDS portfolio equals 20%
- illustrative -
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 23
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0.00%
0.01%
0.10%
1.00%
10.00%
100.00%Equity Class C Class B Class A Super Senior
down-notchedstandardrho = 0
Downgrading by Two Notches – PD Stress
Equity PD Class C PD Class B PD Class A PD Super Senior PDdown-notched 81.66% 23.32% 11.18% 6.93% 2.17%standard 58.51% 6.27% 2.19% 1.11% 0.25%rho = 0 80.37% 0.59% 0.002% 0.00% 0.00%
PD
(Tra
nche
)
- illustrative -
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 24
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Nth-to-Default Distributions – Base Case
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
1 15 29 43 57 71 85 99 113
127
141
155
169
183
197
1st2nd3rd4th5th6th7th8th9th10th
transaction matures after 20 quarters
Frequency
Time (in quarters)
- illustrative -
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 25
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1st/5th-to-Default Distributions
• for equity/1st-to-default investors, assuming a correlation-free world is a conservative approach
• data uncertainty (e.g., ratings/PDs) has huge impact; stress testing and case studies are required
1st-to-default distributions 5th-to-default distributionsFrequency
Time (in quarters)
Frequency
Time (in quarters)
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
1 15 29 43 57 71 85 99 113
127
141
155
169
183
197
standarddown-notchedrho = 0
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
1 15 29 43 57 71 85 99 113
127
141
155
169
183
197
standarddown-notchedrho = 0
- illustrative -
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 26
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Remarks
• a well calibrated model allows for more sophisticated pricing based on the timing of defaults and the
estimated realized loss in case of default occurings
• stress testing for default timing (e.g., front/back-loaded defaults) are important
• stress testing and sensitivity checks on PDs, migration probabilities, recovery values and LGDs, and
other drivers/input parameters are essential
The next slide shows – as our last example – a simple approach to the modeling of stochastic recoveries.
Obviously, the calibration challenge increases with every new complexity in the CDO model.
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 27
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Example: Modeling of Stochastic Recoveries
]0),1(max[ iCOLLCOLLi XCOLL ×+×= σµStochastic Collateral Value:
Variables:• Y state of economy
• COLL value of collateral
• X std. normal random variable
• µ mean collateral value
• σ vola of collateral value• w coupling strength to state of economy
Parametrization Example (CMBS):• µ 100% (conservative if LTVs << 100%)
• σ 7% (21% = 3-std.dev. move; ~ coll. floor at 79%)• w 18% (18% dependency on state of economy)
-4 -2 0 2 40
0.1
0.2
0.3
0.4
ii ZwYwX −+= 1
same Y as in DT simulation ...
- illustrative -
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Concluding Remarks
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 29
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Challenges and Projects
• calibration of copula for default times
• best practice standard approach: Gaussian AVM at 1-y horizon (ri)i=1,...,m and τi = Fi-1(N[ri])
• better: „true“ first passage time (barrier diffusion model)
• problem: FPT density for BM „analytically difficult“ for nonaffine barriers
• speeding up the simulation (traders need it faster ...) by numerical techniques
• risk-neutral valuation: decomposition of spread in credit risky and other parts; e.g.,
• CDO tranches as underlyings have spread contributions from credit risk, liquidity, complexity, ...
• modeling of the „economic cycle“ (autocorrelations, etc.)
• modeling of reinvestments and replenishment
• details like prepayments, work-out time, calibration of stochastic recovery, etc.
• portfolio optimization for CDO issuance (asset selection based on risk contributions ... tranche-dependent)
Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 30
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Remarks
• problems are often on the data side; state of the art in modeling is often too sophisticated compared
to data adequacy and quality of available information
• CDO market evolves very quickly: one always has to catch-up with new structures and developments
• Basel II has a potential to motivate new arbitrage structures/transactions
• better modeling techniques increase profitability, especially in the structured finance market
A more detailled working paper,
CDO Modeling: Techniques, Examples and Applications
is available at www.defaultrisk.com