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Abstract
The intention of this paper is to propose PD calibration framework for low default portfolios (LDP) that allows producing smooth non-zero PD estimates for any given time horizon within the length of economic cycle. The approach produces PDs that are consistent with two main anchors . PIT and TTC PD estimates and are subject to smooth, monotonic transition between those two anchors. In practise, proposed framework could be applied to risk-based pricing of LDP portfolio deals. Moreover, according to the author opinion, the approach is generally compliant with the new IFRS 9 requirements regarding PD term-structure calibration for provisioning.
JEL classification numbers: C01
Keywords: Probability of default, credit risk, PD calibration, risk-based pricing
(ProQuest: ... denotes formulae omitted.)
1 Introduction
Let us assume that some rating system with .. rating grades was implemented in a bank .. years ago. Our task is to calibrate PD for risk-based pricing purposes given available default statistics. Hereinafter we assume that risk part (risk-premium) of a loan-pricing system is based on expected losses equal to PD multiplied by loss-given-default value for a transaction (LGD). LGD part of risk-premium is not covered by the paper, for PD part we assume that PD should be the same for all transactions of a given counterparty.
In case of a low default portfolio (LDP), the most common problems with PD calibration are:
* Unstable (high volatile) historical default rates by rating grades.
* Absence of historical defaults in high-grade (investment grade) rating geades.
* Absence of enough historical default data for PD term-structure calibration.
Despite these LDP portfolio issues, PD calibration approach for risk-based pricing purposes should comply with the following requirements:
. Produce, non-zero monotonic PDs, even if there were no historical default cases in a given rating grade.
. Be able to produce PD-term structure. Deals with different maturities should be assigned different risk-premiums.
. Allow to take into account current market (economic) conditions. Average through-the cycle PD (TTC PD, for details see [1]) produces wrong risk- premiums almost in each point of economic cycle: during expansion periods it overestimates risk-premiums leading to non-market prices and portfolio shrinkage, during recession it underestimates expected defaults leading to uncovered by risk-premiums losses.
. Be transparent to business units: any additional...