Comments on:
Can Structural Models Price Default Risk?
Evidence from Bond and Credit Derivative Markets
by
Jan Ericsson, Joel Reneby and Hoa Wang
Stephen M Schaefer
London Business School
Moody’s Corporation & The Salomon Centre, NYU Stern School of Business
THIRD CREDIT RISK CONFERENCE
New York, 16-17 May 2006
What does the paper find?
1. Leland Toft model:
9 prices CDS reasonably well (on average)
9 but … underestimates bond spreads (> CDS premia)
2. Leland model and Fan Sundaresan model do less well.
3. Liquidity effect:
9 errors in bond spreads: sensitive to liquidity factors
9 errors in CDS: less sensitive to liquidity factors
Comments on Ericsson, Reneby & Wang
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Why I liked the paper
• Shows us that despite a poor press so far (at least
one) structural model has the potential to explain
(at least some) prices
• Good news … (personal view) since structural
models allow us to understand more easily relation
between credit risk and fundamental company
information on assets, asset risk and capital
structure
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Comments: The data
• Sample is quite small:
9 includes only 731 bond-CDS price pairs from 71
entities
9 56% Baa; 26% A
• Bonds and CDS not maturity matched
9 complicates interpretation of differences in pricing
performance
Comments on Ericsson, Reneby & Wang
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Asset Volatility Parameter
• Asset vol. estimates:
9
9
27% [for Leland Toft]
31% [for Leland / Fan Sundaresan]
• Own recent work with Strebulaev (and some previous work
by others) suggests this may be a somewhat high
M ean
M ean
M ean
All
AAA
0.34
0.33
0.22
BB
B
CCC
0.08
AA
A
BBB
Quasi-M arket Leverage
0.16
0.28
0.38
0.52
0.71
0.80
0.23
EquityVolatility
0.26
0.29
0.32
0.43
0.63
0.77
0.22
Estimated Asset Volatility
0.21
0.21
0.21
0.24
0.28
0.34
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and credit exposure highly sensitive to asset volatility
(Leland-Toft Model; parameters as in Leland (2005))
0.250
Default Prob w . Asset Vol =23%
Moody's Default Prob. BBB 1970-2005
Default Prob w . Asset Vol = 27%
Default Probabiity
0.200
0.150
0.100
0.050
0.000
0
5
10
15
20
Horizon
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Why is there a difference in success of model in
explaining CDS vs. Bond spreads?
• Model:
9 No interest rate uncertainty so, for given maturity,
model will give CDS premium and bond spread that
are identical.
9 So differences in model premia / spreads in Table 4
due to:
– Maturity differences between CDS (ave. 4.4 years) and bonds
(ave. 9.4 years)
– CDS premium in model assumed continuous
• For given maturity, since model prices are the same,
difference in errors between bond spread and CDS premia
is just equal to (minus) CDS basis in data
Comments on Ericsson, Reneby & Wang
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CDS vs. Bond Spreads
• In practice, i.e., with uncertain interest rates,
triangular arbitrage between CDS, risky debt and
defaultable debt does not hold exactly
But
• .. holds approximately and market practitioners
will intervene when basis diverges too much from
zero (adjusting for repo rate, funding costs etc.)
• and .. relevant “riskless rate” will be swap rate
rather than Treasury rate
⎛ Difference ⎞
⎜ in errors ⎟ = [Y − Treas] − CDS
⎝
⎠
= [144
Y − Swap
]−CDS
Swap
−Treas
244
3 + [14
4244
3]
- CDS basis
changes over time
Comments on Ericsson, Reneby & Wang
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Difference in pricing errors:
Bond Spread to Treasury – CDS Premium (Credit Rating – A)
120
100
basis points
80
60
40
Bond/Treas Spread - CDS (lhs)
20
0
Jan-99
Jul-99
Jan-00
Jul-00
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… compared to Swap / Treasury Spread (5 Years)
120
100
basis points
80
60
40
Bond/Treas Spread - CDS (lhs)
Swap Treas Spread (lhs)
20
0
Jan-99
Jul-99
Jan-00
Jul-00
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Implications
⎛ Difference ⎞
Y − Swap
Swap
−Treas
]−CDS
⎜ in errors ⎟ = [144
244
3 + [14
4244
3]
⎝
⎠
-CDS basis ≈0 changes over time
• Difference in average error for bond spreads and CDS
most likely due to measurement of bond spreads against
Treasuries rather than against swaps.
• Measured against swaps, model would probably explain
bond spreads and CDS premia about equally well.
• Liquidity exposure of CDS probably more similar to bond
spreads vs. swaps than bond spreads vs. Treasuries.
• And …. strongly endorse basic message: second
generation structural models have great potential to help us
understand credit risk pricing
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