# Combining Risk-Neutral and Real- World Default Probabilities S. Smirnov, A. Kosyanenko, V. Naumenko, V. Lapshin, E. Bogatyreva, S. Afonina Higher School.

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Combining Risk-Neutral and Real- World 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 2 nd best. European Central Bank Take the median or the best linear/convex combination.

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.

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.

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.

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).

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

23 апреля 201012 Combining Homogeneous Estimates Assume that the estimates are unbiased: Given estimated correlation, construct weighted sum with minimal variance.

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.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. 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.