1 A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 A Study of Sellers of Senior Tranched Credit Protection Jon Gregory Quant Congress USA July 8 th 2008
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
A Study of Sellers of Senior Tranched Credit Protection
Jon Gregory
Quant Congress USA
July 8th 2008
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Related Papers
“Credit Tails”, Risk article, January 2008
“A Trick of the Credit Tail”, Risk technical paper, March 2008
“A Free Lunch and the Credit Crunch”, to be published August 2008
“Two Faced Over Counterparty Credit Risk?”, working paper
Please email me at [email protected] for copies of these articles
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
The Failure of the Gaussian Copula Model
MarketGaussian
Copula Model
24.00% 19.3%
82.5 234.7
26.5 82.0
14.0 32.9
8.75 6.99
3.53 0.05
• Dependency is defined by a single correlation parameter
– No concept of idiosyncratic default
– No concept of systemic default
Super Senior 22-100%
Equity 0-3%
3-6%6-9%
12-22%
9-12%
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
CDO Investor Landscape
[0-3%]
[3-7%]
[7-10%]
[10-15%]
[15-30%]And [30-100%]
Rating of counterparty
Risk of underlying
Hedge funds
Aaa rated Monolines
and CDPCs no CSA
Real money investors
under CSA
NR
Baa
Aa
Aaa
SuperAaa
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
The Correlation Skew in Credit
Super Senior 22-100%
Equity 0-3%
3-6%6-9%
Index[0-100%} 12-22%
9-12%
5Y iTraxx Europe
(Investment Grade Corporate Index)
110 bps
[0-3%] 35%
[3-6%] 465 bps
[6-9%] 335 bps
[9-12%} 250 bps
[12-22%] 110 bps
[22-100%] 40 bps
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
0% 5% 10% 15% 20% 25%
Detachment point
Bas
e C
orr
elat
ion
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Into the Super Senior Space
Super Senior 22-100%
Equity 0-3%
3-6%
6-9%
12-22%
9-12%
Each default causes loss of (1-)/125 = 0.48% (40% rec)
22% of losses requires 22% / 0.48% = 46 defaults
5Y [22-100%] pays around 50 bp pa !
-0.100%
0.000%
0.100%
0.200%
0.300%
0.400%
0.500%
0.600%
0.700%
0.800%
19-Mar-07 08-May-07 27-Jun-07 16-Aug-07
22-100%
Long protection on 7Y [22-100%]
(Delta hedged)
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
The Toothpaste Tube Analogy (I)
Super Senior 22-100%
Equity 0-3%
3-6%
6-9%
Index[0-100%]
12-22%
9-12%
Index = Sum of tranches
[22-100%] = [0-100%] – [0-3%] – [3-6%] – [6-9%] – [9-12%] – [12-22%]
• Typically method for extracting super senior
premium implicitly assumes flat correlation curve
up to 5Y
2Y 5Y
[0-3%] 13.52% 25.75%
[3-6%] 3.3 bps 60.5 bps
[6-9%] -1.0 bps 19.5 bps
[9-12%] -0.9 bps 11.0 bps
[12-22%] -0.5 bps 6.0 bps
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Summary of Super Senior Pricing
• We can’t price [22-60%]
• We can’t price tranchelets in the [22-60%] region
• We can’t price bespoke super senior
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
The Toothpaste Tube Analogy (II)• Small changes in equity duration assumptions can change the size of the tube
• Upper bound where [22-100%] is equal to [12-22%] / Lower bound where [22-100%] is worth zero
• Change in 3Y equity premium (or IO/PO prices) moves super senior significantly
0%
10%
20%
30%
40%
50%
0 1 2 3 4 5
Maturity (years)
Eq
uit
y T
ran
che
Exp
ecte
d L
oss
[22-100%] = 4.1 bps [22-100%] = 2.5 bps
Upper bound
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Extrapolation of Base Correlation Curve
• Even if we can price the [22-100%]
– Pricing of 1% wide tranchelets in the [22-60%] region
– Clearly not arbitrage-free
– No value put in the [1-, 100%] part of the capital structure ( is 40% in this case)
0
2
4
6
8
10
12
14
16
18
20
22% 27% 32% 37% 42% 47% 52% 57%
Detachment point
Tra
nch
elet
pre
miu
m (
bp
s)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Bas
e C
orr
elat
ion
Tranchelet Premium Base Correlation Market Points
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Pricing of Bespoke Super Senior• Forced index tranchlets to be arbitrage-free (value distributed equally within [22-60%])
• On a portfolio which is 14% more risky, common scaling techniques introduce arbitrage
• On a more risky portfolio this potentially becomes worse
0
2
4
6
8
10
12
14
16
22.0% 27.0% 32.0% 37.0% 42.0% 47.0% 52.0% 57.0%
Detachment point
Tra
nch
elet
pre
miu
m (
bp
s)
index
bespoke
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Packaging Super Senior Risk
• Leveraged super senior (LSS) trades
– A leveraged transaction with a defined trigger event
• Credit derivative product companies (CDPC)
– Like a more complex LSS
– Trigger is not so well defined
– CDPC has multiple counterparties
• Monoline insurer
– Similar to CDPC but will insurer other financial risks also
– Should benefit from diversification
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Leveraged Super Senior Illustration
× Leverage
• Super senior tranche pays small premium
• Leverage this (typically around 10 times)
• Create a structure paying a ‘good’ premium referenced to a default remote
tranche
• Investor loss will come when structure deleverages
– Investor may have option to post more collateral
– Alternatively an unwind will occur
Collateral
UncollateralizedPortion
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Rating Super Senior Risk
• Packaging super senior tranches can always be made to look
like triple-A counterparty risk
Super senior tranche(Triple-A)
Packaged Super senior tranche (at least Triple-A)
Capital (share) of monoline / CDPC etc
()
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
LSS Unwind Triggers• Loss only trigger
– Simple to rate (default risk only, like a CDO tranche)
– Issuer retains spread and implied correlation risk
• Spread (+ loss) triggers
– More complex to rate (includes spread dynamics in rating model)
– Issuer retains implied correlation risk
• Market value triggers
– Very hard to rate (only one rating agency DBRS have ever done so)
– Issuer retains only gap risk
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Leveraged Super Senior Pricing Argument
• There is around $200+ billion of leveraged super senior protection out there
• Issuers seem to price via the equivalence argument
• Advantage is that we simple argue that gap risk is very small
– Example : at 10 times leverage, a market value trigger of 5% is ‘safe’
• This is a standard argument applied to lots of leveraged products (CPPI etc, ….)
• This argument is wrong for LSSLSS Protection value = SS Protection value Leverage – Gap Risk
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
LSS Protection Valuation Bounds
Perfect
trigger
No trigger
“Gap Risk”
[A, B] Upper Bound
LSS Value??
× L
[A, A+] Lower Bound
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
LSS Pricing
Denote
– trigger time by
– initial collateral by
T
t
BAs sdMstBE )(),(1 ,
Trigger ?
T
t
BAT VtBE )),(min(),(1 ,
No
Yes
Standard tranche protection
Settle contract with cap at collateral value
leverageAB /)(
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
LSS Pricing (II)
T
t
BAT
T
t
BAT
T
t
BAs
T
t
AAs
T
t
BAT
T
t
BAs
VtBE
VtBE
sdMstBE
sdMstBE
VtBEsdMstBE
))()(,(1
)(),(1
)(),(1
)(),(1
)),(min(),(1)(),(1
,
,
,
,
,,
Collateralised Protection
De-leverage value
Unwind value
Gap option
= 0
Even if client has option to deleverage then it is suboptimal
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Formal Valuation
T
t
BAT
T
t
AAs
T
t
BAT
T
t
BAT
T
t
AAs
VtBEsdMstBE
VtBE
VtBE
sdMstBE
)),(min(),(1)(),(1
))()(,(1
)(),(1
)(),(1
,,
,
,
,
• Setting de-leverage term to zero
Lower Bound Trigger Option
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Leveraged Super Senior Overview
[A, B] Upper Bound
[A, A+] Lower Bound
Perfect trigger
No trigger
“Gap Risk”
“Trigger Option”
Actual LSS Value
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Pricing the Trigger Option
),(1)),(min(),(1 , tBEVtBE T
T
t
BAT
• Pricing (and hedging!) the trigger option is not easy
– Out of the money tranche option payoff
• But we can get some insight in the loss only trigger case
– Here we can overhedge with a contract paying at the loss trigger K
– This is simply a digital CDO tranche
• This effectively sets a maximum leverage independent of gap risk
AB
tV
tVtleverage
BA
KK
)(
)()(
,
,*
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Example
• For the (5Y) tranche markets as shown
• We calculation the maximum leverage for
– A [22-100%] LSS structure
– 5-year maturity
– With a loss trigger as a function of loss trigger level
4th May 2005 19th March 2007 4th December 2007
Index 44 25 53[0-3%] 29.00% 11.87% 25.05%[3-6%] 168 54.5 156.3[6-9%] 49 14.8 85[9-12%] 25 6.8 60[12-22%] 16 2.8 34[22-100%] 5.5 2.4 15.0
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Maximum Leverage
0
5
10
15
20
25
30
35
40
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Loss Trigger
Max
imu
m L
ever
age
4th May 2005 19th March 2007 4th December 2007
• Leverage Super Senior Pricing is not a gap risk problem!
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Monolines and CDPCs
• Capital model
– (Tranche) Ratings driven run on a daily basis
– Capital (less any losses) must be above capital required by model to
support Aaa rating
• Operating modes (CDPC / monoline)
– Normal operating mode / Triple-A rating
– Suspension mode / downgrade
– Wind-down mode / Run-off
Required capital
Aaa attachment
Ratings driven loss distribution
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
Monoline / CDPC Comparison with LSS
NormalState
RestrictedState
Wind-downState
Trigger Not Hit
< 6 months
Losses to tranches
TriggerHit
Full Deleverage(unwind)
Losses to tranches
Monoline / CDPC Leverage Super Senior
De-
leve
rage
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A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008
CDPC / Monoline Purchased Protection
[A, B] Upper Bound
[A, A+] Lower Bound for LSS
“Counterparty Risk”
No value
Impact of effective leverage