Synthetic CDOs: Industry Trends in Analytical and Modeling Techniques By: Lawrence Dunn...

Synthetic CDOs: Industry Trends in Analytical and Modeling Techniques

By: Lawrence Dunn

[email protected]

1-212-981-1060

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

Modeling Synthetic CDOs

» Conditional independence technique• No complicated waterfall• A few simplifying assumptions• Uses market observations• Results in explicit, quick-to-compute expressions

for the mark-to-market value of synthetics


» Model Inputs and Outputs

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


» Implications of Synthetic Model• Industry Standard Model – Universal Language

Between 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

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

Methodology Overview – loss distribution

•Structural 1-factor correlated default model•For each obligor j:

» Asset value modeled as a random variable that’s a function of a market factor variable, an idiosyncratic variable, and correlation:

where default signaled by Zj dipping under threshold j

» To get j, start with term structure of CDS spreads» Derive one hazard rate per CDS spread» Calculate the obligor’s probability of default for a given

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

falling below j in terms of j dipping below a function of j, , and the fixed z

jj ZZ 21

Methodology Overview – loss distribution

•For each obligor j (cont’d):» That relationship allows us to get the conditional default

probability of the obligor

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

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

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

21)(

zzp j

j21

zjj

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

Portfolio loss

Pro

babi

lity

corr=25%


0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

Portfolio loss

Pro

babi

lity

corr=10%corr=25%


0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

Portfolio loss

Pro

babi

lity

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

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

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

50%

60%

70%

Correlation

Upf

ront

spr

ead

(bp)


0% 5% 10% 15% 20% 25% 30%440

465

490

515

540

Correlation

Tra

nche

fai

r sp

read

(bp

)


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

60

120

180

240

Correlation

Tra

nche

fai

r sp

read

(bp

)


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

25

50

75

100

Correlation

Tra

nche

fai

r sp

read

(bp

)


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

5

10

15

20

Correlation

Tra

nche

fai

r sp

read

(bp

)

Compound correlation skew

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

15%

30%

45%

60%

Detachment point

Cor

rela

tion

CompoundBase

Base correlations are more smooth.

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

15%

30%

45%

60%

Detachment point

Cor

rela

tion

CompoundBase

Summary

» Quick valuation of synthetics and other reasons 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

Synthetic CDOs: Industry Trends in Analytical and Modeling Techniques By: Lawrence Dunn...

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