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Synthetic CDOs: Industry Trends in Analytical and Modeling Techniques
By: Lawrence Dunn
1-212-981-1060
slide 2
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
slide 3
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
slide 4
Modeling Synthetic CDOs
» Model Inputs and Outputs
slide 5
Modeling Synthetic CDOs
» Model Inputs and Outputs
slide 6
Modeling Synthetic CDOs
» Model Inputs and Outputs
slide 7
Modeling Synthetic CDOs
» Model Inputs and Outputs
slide 8
Modeling Synthetic CDOs
» Model Inputs and Outputs
slide 9
Modeling Synthetic CDOs
» Model Inputs and Outputs
slide 10
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
slide 11
Modeling Synthetic CDOs
» 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
slide 12
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
slide 13
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
slide 14
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
slide 15
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%
slide 16
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=10%corr=25%
slide 17
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=10%corr=25%corr=40%
slide 18
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)
slide 19
Trac-X NA IG, 3-7% trancheMarch 12, 2004
0% 5% 10% 15% 20% 25% 30%440
465
490
515
540
Correlation
Tra
nche
fai
r sp
read
(bp
)
slide 20
Trac-X NA IG, 7-10% trancheMarch 12, 2004
0% 5% 10% 15% 20% 25% 30%0
60
120
180
240
Correlation
Tra
nche
fai
r sp
read
(bp
)
slide 21
Trac-X NA IG, 10-15% trancheMarch 12, 2004
0% 5% 10% 15% 20% 25% 30%0
25
50
75
100
Correlation
Tra
nche
fai
r sp
read
(bp
)
slide 22
Trac-X NA IG, 15-30% trancheMarch 12, 2004
0% 5% 10% 15% 20% 25% 30%0
5
10
15
20
Correlation
Tra
nche
fai
r sp
read
(bp
)
slide 23
Compound correlation skew
0% 5% 10% 15% 20% 25% 30%0%
15%
30%
45%
60%
Detachment point
Cor
rela
tion
CompoundBase
slide 24
Base correlations are more smooth.
0% 5% 10% 15% 20% 25% 30%0%
15%
30%
45%
60%
Detachment point
Cor
rela
tion
CompoundBase
slide 25
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