Predicting and Valuing Default
Approaches
1. Empirical Method.
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Relies on financial/accounting data.
Picks up patterns in history: what
accounting.structures prevail before defaults?
2. Structural Method.
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Relies on Stock Market data.
Variations on the seminal Merton Model.
3. Reduced Form Method.
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Relies on Bond Market data.
Relativistic framework (a la BDT for IR
modeling).
Empirical Method Failures
The Enron and Worldcom bankruptcies in 2001
highlight a fundamental problem with the
empirical method. It is backward looking--both
in terms of patterns relating accounting data to
default and in terms of the actual data itself.
Moodys Case Studies:
– Enron
– Worldcom
– Bally's
Market-Adjusted Ratings
Moody’s notes that the standard bond ratings
process may not be as accurate or timely as
market-based information.
They now market a product called Market Implied
Ratings (MIR):
Moodys MIR
Structural Model in Practice
Merton’s model (also known as the Black-Scholes
Model) is the benchmark structural model. All of
the relevant information about the default risk of
the company, and the price of that risk is
contained in the stock market.
In practice, the Moodys KMV model is probably
the most widely used variant. While the KMV
model is proprietary, much has been written about
it by Moodys economists.
KMV Features
– The benchmark riskfree rate is the swap curve--not the
Treasury curve.
– There is time-varying market risk premium.
– There is a liquidity premium based on the firm’s access to
capital markets.
– Expected Recovery is time-varying.
– Equity is treated as a perpetual down-and-out option on the
firm’s assets.
– Bankruptcy trigger is a percentage (e.g., 70%) of total firm
liabilities.
– The translation from the EqRNW default probability to the
physical probability is made by comparing the two
historically.
Reduced Form Model
A popular reduced form model is that of Hull and White.
The term structure of EqRNW default probabilities is
obtained from a series of Corporate and Treasury bonds.
Example:
5-Year 0-coupon Treasury yields 5%.
5-Year 0-coupon Corporate yields 5.5%
T = 100 exp(-.05 5) = 77.8801
C = 100 exp(-.055 5) = 75.9572
PV of cost of default = $1.9229.
If we assume 0 recovery on default, then:
100 (p) (exp(-.05 5) = 1.9229, where p is the EqRNW probability of
default.
p = 2.47%.
Hull White Model
Since there few 0-coupon corporates, the
implementation of the model entails
bootstrapping both the Treasury and Corporate
yield curves. Also, recovery is not 0, so the
recovery rate would be estimated using relevant
historical data.
Comparing Models
Here’s a link to a 2005 study from KMV that
compares the Merton, Moodys KMV, and
Hull-White models in terms of their ability
to explain Credit Default Swap spreads.
It is intriguing that the KMV model -- which
uses stock market information--does a better
job than the Hull and White model which
uses bond market information.