Transcript Combining Risk-Neutral and Real-World Default Probabilities S

Combining Risk-Neutral and RealWorld Default Probabilities
S. Smirnov, A. Kosyanenko,
V. Naumenko, V. Lapshin,
E. Bogatyreva, S. Afonina
Higher School of Economics, Moscow
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.
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.
Reported Results
• Kealhofer (2003): using several estimates does
not improve quality.
• Löffler (2007): using several estimates does
improve quality.
Basel II Recommendations
• 2 estimates => take the minimum;
• 3 estimates => take the middle;
• more estimates => take the 2nd best.
European Central Bank
• Take the median or the best linear/convex
combination.
The Econometric Model
• Takes weighted sum of factors PD  F   i Ai 
 i

F () - logit/prob it function
i - coefficien ts Ai - discretize d factor val ues
• We use the current Agency for Deposit
Insurance set of coefficients and parameters.
• It has its drawbacks, but it also has the
semiofficial status.
The Market Model
• Risky bond prices are determined via the riskneutral mathematical expectation and noarbitrage argument:
(1  p)e
•
•
•
•
( r  y )t
 Rpe
( r  y )t
e
rt
R – recovery rate;
P – default probability during the time t;
r – risk-free yield;
y – credit spread.
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.
q  pRisk Neutral  pReal  p
q  p  Risk  (Market price of risk )
Risk-Neutral to Real
• No universally accepted solution.
• Kaelhofer (2003): one-factor model
 qt
N 
2
1
1

1  pt 
2
  N  2 t

 
• Compatible with Merton and CAPM models.
• Easy interpretation of  : relative excess
 r


return
(r – risk-free rate).

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.
Estimated Parameter Value
Combining Homogeneous Estimates
• Assume that the estimates are unbiased:
p1  p  11 , p2  p   2 2 , corr (1 ,  2 )  
• Given estimated correlation, construct
weighted sum with minimal variance.
var p1  (1   ) p2   min


p
2
2




  1 2  p1     1 2  p2
 12   22  2 1 2 
23 апреля 2010
2
1
12
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?
Negative correlations
• Some banks exhibit strongly negative (< -0.5)
correlations between market and econometric
PDs.
•
•
•
•
•
Международный Промышленный Банк
АКИБанк
Банк 'Россия'
СтройКредитБанк
ГлобэксБанк
• Reported statistics has been tampered with?
References
1.
2.
3.
4.
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.
Tabakis E.,Vinci A. Analysing and combining multiple credit assessments
of financial institutions, 2002, ECB working paper.
Löffler G. “The Complementary Nature of Ratings and Market-Based
Measures of Default Risk.”// Journal of Fixed Income. 2007-Vol. 17-pp.
38-47.
Kealhofer, S. Quantifying credit risk I/II: Default prediction //Financial
Analysts Journal. – 2003.- Vol. 59, No. 3. pp. 30-44, 78-92.
Thank you for your attention