Sparse Structural Approach for Rating Transitions

Abstract

In banking practice, rating transition matrices have become the standard approach of deriving multi-year probabilities of default (PDs) from one-year PDs, the latter normally being available from Basel ratings. Rating transition matrices have gained in importance with the newly adopted IFRS 9 accounting standard. Here, the multi-year PDs can be used to calculate the so-called expected credit losses (ECL) over the entire lifetime of relevant credit assets.

A typical approach for estimating the rating transition matrices relies on calculating empirical rating migration counts and frequencies from rating history data. For small portfolios, however, this approach often leads to zero counts and high count volatility, which makes the estimations unreliable and unstable, and can also produce counter-intuitive prediction patterns such as non-parallel/crossing forward PD patterns.

This paper proposes a structural model which overcomes these problems. We make a plausible assumption of an underlying autoregressive mean-reverting ability-to-pay process. With only three parameters, this sparse process can well describe an entire typical rating transition matrix, provided the one-year PDs of the rating classes are specified (e.g. by the rating master scale).

The transition probabilities produced by the structural approach are well-behaved by design. The approach significantly reduces the statistical degrees of freedom of the estimated transition probabilities, which makes the rating transition matrix more reliable for small portfolios. The approach can be applied to data with as few as 50 observed rating transitions. Moreover, the approach can be efficiently applied to data consisting of continuous PDs (prior to rating discretization).

In the IFRS 9 context, the approach offers an additional merit: it can easily account for the macroeconomic adjustments, which are required by the IFRS 9 accounting standard.

Keywords: Multi-year, Lifetime, Probability of Default, PD, Default Rates, Rating Transition Matrices, IFRS 9, Expected Credit Losses, ECL, Through-the-Cycle, TTC, Point-in-Time, PIT, Macroeconomic Adjustments, Time Series, Autoregression, Accounting, Financial Instruments, Maximum Likelihood Estimation

JEL Classification: C13, C11, C22, C51, C53, E32, E37, M41, G33