Combining Risk-Neutral and Real-World Default Probabilities

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Combining Risk-Neutral and Real-World Default
Probabilities

• S. Smirnov, A. Kosyanenko, V. Naumenko, V.
  Lapshin, E. Bogatyreva, S. AfoninaHigher School
  of Economics, Moscow

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Basel II

• 417. p.93. Credit scoring models and other
  mechanical rating procedures generally use only a
  subset of available information. Although
  mechanical rating procedures may sometimes avoid
  some of the idiosyncratic errors made by rating
  systems in which human judgement plays a large
  role, mechanical use of limited information also
  is a source of rating errors.
• 417. p.94. The bank must have in place a process
  for vetting data inputs into a statistical
  default or loss prediction model which includes
  an assessment of the accuracy, completeness and
  appropriateness of the data specific to the
  assignment of an approved rating.
• 462. p.102. Banks may have a primary technique
  and use others as a point of comparison and
  potential adjustment. Supervisors will not be
  satisfied by mechanical application of a
  technique without supporting analysis.

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Why and How to Combine Different Estimates?

• A European Central Bank working paper (2002)
  addresses this issue.
• Combining multiple assessments to produce one
  single benchmark assessment is a vital problem
  faced, for example, when assessments appear to be
  near or below certain important thresholds set by
  supervisors, central banks or counterparties of
  financial transactions. Basel II has touched on
  this issue, but the problem needs further study.

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Reported Results

• Kealhofer (2003) using several estimates does
  not improve quality.
• Löffler (2007) using several estimates does
  improve quality.

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Basel II Recommendations

• 2 estimates gt take the minimum
• 3 estimates gt take the middle
• more estimates gt take the 2nd best.
• European Central Bank
• Take the median or the best linear/convex
  combination.

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The Econometric Model

• Takes weighted sum of factors
• We use the current Agency for Deposit Insurance
  set of coefficients and parameters.
• It has its drawbacks, but it also has the
  semiofficial status.

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The Market Model

• Risky bond prices are determined via the
  risk-neutral mathematical expectation and
  no-arbitrage argument
• R recovery rate
• P default probability during the time t
• r risk-free yield
• y credit spread.

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Our Problem

• One estimate is real-world received with an
  econometric default forecast model.
• The other estimate is risk-neutral received via
  expected value argument from bond market prices.

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Risk-Neutral to Real

• No universally accepted solution.
• Kaelhofer (2003) one-factor model
• Compatible with Merton and CAPM models.
• Easy interpretation of relative excess
  return (r risk-free rate).

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Parameter Estimation

• The model has a single parameter to be estimated
  from real data.
• Little accuracy is needed the two estimates are
  not identical, they are based on different data
  and just need to be brought to a common base.

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Estimated Parameter Value
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Combining Homogeneous Estimates

• Assume that the estimates are unbiased
• Given estimated correlation, construct weighted
  sum with minimal variance.

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Negative Market Prices of Risk

• During 08.2007 12.2008 the econometric
  (real-world) PD was higher than the market
  (risk-neutral) PD.
• The market did not react to high PDs?
• The econometric statistics was wrong?
• Some external force kept bond prices high?

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Negative correlations

• Some banks exhibit strongly negative (lt -0.5)
  correlations between market and econometric PDs.
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• Reported statistics has been tampered with?

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References

1. Basel Committee on Banking Supervision.
   International Convergence of Capital Measurement
   and Capital Standards. A Revised Framework. Bank
   for International Settlements. June 2006.
   http//www.bis.org/publ/bcbs128.pdf.
2. Tabakis E.,Vinci A. Analysing and combining
   multiple credit assessments of financial
   institutions, 2002, ECB working paper.
3. Löffler G. The Complementary Nature of Ratings
   and Market-Based Measures of Default Risk.//
   Journal of Fixed Income. 2007-Vol. 17-pp. 38-47.
4. Kealhofer, S. Quantifying credit risk I/II
   Default prediction //Financial Analysts Journal.
   2003.- Vol. 59, No. 3. pp. 30-44, 78-92.

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• Thank you for your attention
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