Finance and Credit

A two-parameter formula of default probability term structure

Vol. 24, Iss. 8, AUGUST 2018

Received: 14 June 2018

Received in revised form: 2 July 2018

Accepted: 17 July 2018

Available online: 29 August 2018

Subject Heading: Financial control

JEL Classification: C58, G17, G28

Pages: 1920–1937

Pomazanov M.V. National Research University Higher School of Economics, Moscow, Russian Federation

Importance This paper describes the existing methods of default probability term structure modeling and the disadvantages that limit their application.
Objectives The paper aims to give an effective offer to lenders on the construction of a method of estimating the probability of default of a corporate borrower, taking into account the changed term to the end of the credit transaction, not contradicting the new IFRS 9 standard.
Methods For the study, I used an economic and statistical analysis, and optimization of parameters of special kind of distributions on statistical data of rating agencies.
Results Using the consolidated empirical data of rating agencies, I attribute a two-parameter formula of default probability term structure, which does not contradict the requirements of the international standard IFRS 9 for the corporate borrowers sector, that does not have enough internal data to build its own Lifetime PD internal model.
Conclusions and Relevance The presented study substantiates the formula of calculation of a default probability term structure in the best fitting distribution pool. It is calibrated on external empirical and statistical data of rating agencies, including a 44-year period. The formula is explicit and does not require complex computations. The results obtained can be used to calculate the rate of reserves for credit assets, estimate the minimum (break-even) lending rate taking into account the risk and the term of the transaction, optimize the term of the transaction, and for other possible applications.

Keywords: credit risk, IFRS reserves, default probability, default time structure, IFRS 9


  1. Merton R.C. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. The Journal of Finance, 1974, vol. 29, iss. 2, pp. 449–470. URL: Link
  2. Vasicek O. Loan Portfolio Value. Risk, 2002, December, pp. 160–162.
  3. Gürtler M., Heithecker D. Multi-Period Defaults and Maturity Effects on Economic Capital in a Ratings-based Default-mode Model. Working Papers Technische Universität Braunschweig, Institute of Finance, 2005, no. FW19V2. URL: Link
  4. Fisher E., Heinkel R., Zechner J. Dynamic Capital Structure Choice: Theory and Tests. The Journal of Finance, 1989, vol. 44, no. 1, pp. 19–40. URL: Link
  5. Duffie D., Lando D. Term Structure of Credit Spreads with Incomplete Accounting Information. Econometrica, 2001, vol. 69, iss. 3, pp. 633–664. URL: Link
  6. Kiefer N.M., Larson C.E. Counting Processes for Retail Default Modeling. Journal of Credit Risk, 2015, vol. 11, iss. 3, pp. 45–72. URL: Link
  7. Cox D.R. Regression Models and Life-Tables. Journal of the Royal Statistical Society. Series B (Methodological), 1972, vol. 34, no. 2, pp. 187–220. URL: Link
  8. Breeden J. Reinventing Retail Lending Analytics – 2nd Impression – Forecasting, Stress Testing, Capital and Scoring for a World of Crises. London, Risk Books, 2010, 433 p.
  9. Israel R.B., Rosenthal J.S., Wei J.Z. Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings. Mathematical Finance, 2001, vol. 11, iss. 2, pp. 245–265. URL: Link
  10. Brunel V., Roger B. Le Risque de Credit: Des Modeles au Pilotage des Banques. Economica, 2014.
  11. Brunel V. Loan Classication under IFRS 9. Risk, 2016, May, pp. 77–80.
  12. Bluhm C., Overbeck L. Calibration of PD Term Structures: To Be Markov or Not To Be. Risk, 2007, vol. 20, no. 11, pp. 98–103. URL: Link
  13. Kristof T., Virag M. Lifetime Probability of Default Modeling for Hungarian Corporate Debt Instruments. URL: Link
  14. VaněkT., Hampel D. The Probability of Default under IFRS 9: Multi-period Estimation and Macroeconomic Forecast. Acta Univ. Agric. Silvic. Mendelianae Brun, 2017, vol. 65, iss. 2, pp. 759–776. URL: Link
  15. Petrov D., Pomazanov M. Validation Method of Maturity Adjustment Formula for Basel II Capital Requirement. The Journal of Risk Model Validation, Risk Journals, 2009, vol. 3, iss. 3, pp. 81–97.
  16. Marshall A.W., Olkin I. Life Distributions. New York, Springer, 2007, 783 p.
  17. Karminskii A. [Corporate rating models for emerging markets]. Korporativnye finansy = Journal of Corporate Finance Research, 2011, vol. 5, iss. 3, pp. 19–29. (In Russ.) URL: Link

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