cdo techniques june08 04

8/9/2019 CDO Techniques June08 04

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Synthetic CDOs: IndustryTrends in Analytical and

Modeling Techniques

By: Lawrence Dunn

[email protected]

1-212-981-1060


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Synthetic CDOs: Reasons for Popularity

Quick Valuations & Sensitivities

Transparency: no complicated waterfalls

Liquidity: will be further fueled by single tranche

synthetics and tranched Trac-x and IBoxx indices No need to place full structures


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Modeling Synthetic CDOs

Conditional independence technique

No complicated waterfall

A few simplifying assumptions

Uses market observations

Results in explicit, quick-to-compute expressionsfor the mark-to-market value of synthetics


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Model Inputs and Outputs


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Model Features and Practical Uses

Fast seconds, not minutes/hours

Accurate no simulation error

Practical Uses for Valuations

Marking books

Deciding fair bid/offer

Practical Uses for Sensitivities

Investors tailor credit views

Dealers manage book, offer single tranches


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Implications of Synthetic Model

Industry Standard Model Universal LanguageBetween Dealers and Investors

The Black-Scholes of the structured credit market Implied Correlation

Sensitivities (the Greeks)

Influence on Cash Flow CDO Valuation

Pull to True Monte Carlo

Consistency Across Names and Correlations

Boost Primary and Secondary Markets


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Methodology Overview

For each tranche:

MTM = Exp(premium) Exp(loss)

Use collateral info to model the losses

Exp(loss)

~ directly from loss distribution

Exp(premium)

~ spread x remaining notional on each pay date~ remaining notional is function of loss distribution


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Methodology Overview loss distribution

Structural 1-factor correlated default model

For each obligor j:

Asset value modeled as a random variable thats afunction of a market factor variable, an idiosyncraticvariable, and correlation:

where default signaled by Zj dipping under threshold Ej To get Ej, start with term structure of CDS spreads

Derive one hazard rate per CDS spread

Calculate the obligors probability of default for a given

payment date Notice that if we fix the value of Z, then we can rewrite Zj

falling below Ej in terms ofIj dipping below a function ofEj, [, and the fixed z

jj ZZ I[[21 !


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Methodology Overview loss distribution

For each obligor j (contd):

That relationship allows us to get the conditional defaultprobability of the obligor

Using probability generating functions, generatingfunctions for loss, convolution, and FFT, you can derivep(k|z), the conditional loss probability; specifically theprobability of losing k units of base loss

Integrate over all values of z to turn your conditional lossprobability into an unconditional loss probability p(k)

Finally these p(k) get you Exp(Loss)

*

21

)([

[E zzp

j

j

21 [

[E

I

zj

j


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Trac-X NA IG -- March 12, 2004Index=70; Rec=40%; EL=3.4%

0 5 10 15 20 25 300

0.05

0. 1

0.15

0. 2

0.25

Portfol io loss

Probability

corr=25%


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0 5 10 15 20 25 300

0.05

0. 1

0.15

0. 2

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Portfol io loss

Probability

corr=10%corr=25%


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0 5 10 15 20 25 300

0.05

0. 1

0.15

0. 2

0.25

Portfol io loss

Probability

corr=10%corr=25%corr=40%


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Trac-X NA IG, 0-3% trancheMarch 12, 2004

0% 5% 10% 15% 20% 25% 30%40 %

50 %

60 %

70 %

Correlation

Upfrontspread

(b

p)


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0% 5% 10% 15% 20% 25% 30%44 0

46 5

49 0

51 5

54 0

Correlation

Tranche

fairspread

(bp)


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0% 5% 10% 15% 20% 25% 30%0

60

12 0

18 0

24 0

Correlation

Tranche

fairspread

(bp)


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0% 5% 10% 15% 20% 25% 30%0

25

50

75

10 0

Correlation

Tranche

fairspread

(bp)


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0% 5% 10% 15% 20% 25% 30%0

5

10

15

20

Correlation

Tranche

fairspread

(bp)


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Compound correlation skew

0% 5% 10% 15% 20% 25% 30%0%

15 %

30 %

45 %

60 %

Detachm ent po in t

Correlation

CompoundB a se


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Base correlations are more smooth.

0% 5% 10% 15% 20% 25% 30%0%

15 %

30 %

45 %

60 %

Detachm ent po in t

Correlation

CompoundB a se


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Summary

Quick valuation of synthetics and otherreasons for their popularity

Conditional independence technique

Model inputs and outputs

Features and practical uses

Implications to marketplace

Methodology overview

Interesting Case: NA IG Trac-x

cdo techniques june08 04

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