Predicting and Valuing Default

1
Predicting and Valuing Default
2
Approaches

• Empirical Method.
• Relies on financial/accounting data.
• Picks up patterns in history what
  accounting.structures prevail before defaults?
• Structural Method.
• Relies on Stock Market data.
• Variations on the seminal Merton Model.
• Reduced Form Method.
• Relies on Bond Market data.
• Relativistic framework (a la BDT for IR modeling).

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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

4
Market-Adjusted Ratings

• Moodys 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

5
Structural Model in Practice

• Mertons 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.

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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 firms
  access to capital markets.
• Expected Recovery is time-varying.
• Equity is treated as a perpetual down-and-out
  option on the firms 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.

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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.

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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.

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Comparing Models

• Heres 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.