  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. 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.
