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GCP Collateralized Debt Obligations Autumn School on Risk Management October 02, 2003 Modeling and Evaluation Christian Bluhm Group Credit Portfolio Management GCP3 - Structured Finance Analytics HypoVereinsbank Sederanger 5 D-80538 Munich, Germany phone 089-378/46033 email [email protected] This talk reflects the opinion of the author and not the opinion of HypoVereinsbank.

CDO Modeling C. Bluhm

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Page 1: CDO Modeling C. Bluhm

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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.

Page 2: CDO Modeling C. Bluhm

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

Page 3: CDO Modeling C. Bluhm

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CDOs: Motivation, Structures, and Trends

Page 4: CDO Modeling C. Bluhm

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

Page 5: CDO Modeling C. Bluhm

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)

Page 6: CDO Modeling C. Bluhm

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)

Page 7: CDO Modeling C. Bluhm

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.

Page 8: CDO Modeling C. Bluhm

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)

Page 9: CDO Modeling C. Bluhm

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

Page 10: CDO Modeling C. Bluhm

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The Mathematics of CDOs

Page 11: CDO Modeling C. Bluhm

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.

Page 12: CDO Modeling C. Bluhm

Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 12

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Choice of Portfolio Model

Page 13: CDO Modeling C. Bluhm

Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 13

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Default Times from Credit Curves

Page 14: CDO Modeling C. Bluhm

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

Page 15: CDO Modeling C. Bluhm

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

Page 16: CDO Modeling C. Bluhm

Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 16

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Multivariate Default Times Distribution

Page 17: CDO Modeling C. Bluhm

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.

Page 18: CDO Modeling C. Bluhm

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

Page 19: CDO Modeling C. Bluhm

Christian Bluhm · HypoVereinsbank Munich · Group Credit Portfolio Management (GCP3) – Structured Finance Analytics · Page 19

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Page 20: CDO Modeling C. Bluhm

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A Random Walk Through SomeExamples and Applications

Page 21: CDO Modeling C. Bluhm

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 -

Page 22: CDO Modeling C. Bluhm

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 -

Page 23: CDO Modeling C. Bluhm

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 -

Page 24: CDO Modeling C. Bluhm

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 -

Page 25: CDO Modeling C. Bluhm

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 -

Page 26: CDO Modeling C. Bluhm

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.

Page 27: CDO Modeling C. Bluhm

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 -

Page 28: CDO Modeling C. Bluhm

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Concluding Remarks

Page 29: CDO Modeling C. Bluhm

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)

Page 30: CDO Modeling C. Bluhm

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