Point-in-time (PIT) and through-the-cycle (TTC) rating philosophies are both firmly established in credit risk management, yet their conceptual differences are often handled without a unified modelling framework. Based on the recent work by Kalkbrener and Packham [2026], this article provides a formal characterization of PIT and TTC properties in terms of rating migrations and default behaviour, clarifying where cyclicality enters a rating system and how this affects default probabilities over different time horizons. The underlying mathematical model of rating migration processes explicitly conditions credit ratings on economic states to reflect the impact of macroeconomic developments on default rates. A stylised example illustrates how PIT and TTC ratings coexist within a single framework and how their long-run behaviour can be aligned.
1. PIT and TTC ratings in practice
For banks, insurers, and supervisors, credit ratings are a key input into probability of default (PD) estimation, which is essential for expected credit loss (ECL) calculations, capital requirements and portfolio risk monitoring. From a risk management perspective, PIT and TTC ratings address different regulatory and accounting requirements. TTC ratings are central to regulatory capital frameworks, where stability across the business cycle is essential to limit procyclicality [Borio et al., 2001; Basel III: CRR/CRD]. PIT ratings, by contrast, are better suited for expected credit loss calculations under IFRS 9 and CECL, where current and forward-looking macroeconomic information must be reflected explicitly [IFRS 9; FASB ASU 2016-13].
Both external and internal rating systems are often hybrid systems. Ratings react to macroeconomic developments, but not fully or instantaneously; default rates of rating grades vary over time; and probabilities of default (PDs) are often transformed between PIT and TTC representations depending on the use case [see e.g. Altman & Rijken, 2004; Gordy & Howells, 2004]. However, no precise mathematical definition of PIT and TTC characteristics of rating systems has been established in the literature. The main objective of the article summarised here is to develop a mathematical framework for rating migration processes that factors in the economic situation and therefore allows for a formal characterisation of PIT and TTC ratings.
2. Economic conditioning of rating migrations
Our approach builds on the generally accepted claim that default rates and rating migrations depend on macroeconomic conditions [Wilson, 1998; Nickell et al., 2000; Bangia et al., 2002]. Rather than assuming a single unconditional migration matrix, we specify rating transition matrices conditional on an economic state process. As a consequence, the stand-alone rating process is typically no longer a Markov process, which is consistent with earlier empirical findings that observed rating transitions violate the Markov property [Altman, 1998; Lando & Skødeberg, 2002; Güttler & Raupach, 2010]. However, it is a key assumption in our model that the economic state process as well as the joint process of economic state and rating state are (time-homogeneous) Markov processes. In other words, the rating process becomes Markovian if its state space is extended to the product space consisting of economic states and rating classes. This property facilitates the application of methods from Markov theory to approximate the rating migration process by a time-inhomogeneous Markov chain [see also Bluhm and Overbeck, 2007] and to derive the rating process’ asymptotic behaviour.
3. Formal distinction between PIT and TTC behaviour
Within this setup, PIT and TTC rating philosophies can be characterized precisely:
PIT ratings are explicitly assigned according to a firm’s PD, reflecting not only firm-specific aspects but also the macroeconomic environment. As a consequence, the expected one-period default probability of a PIT rating grade does not depend on the economic state since the rating itself already factors in the relevant economic information. Cyclicality therefore enters primarily through rating migrations. This interpretation aligns closely with accounting-driven PD concepts used under IFRS 9 and CECL [Aguais et al., 2008; Miu & Ozdemir, 2017].
TTC ratings have a firm-specific character and are defined by rating migrations that are independent of economic states (conditional on survival). Rating stability is achieved by construction, while expected default probabilities of TTC rating grades vary over the cycle. This is in contrast to TTC default probabilities found in practice, which are often based on “stressed” PDs, i.e., PDs under a specific economic state, and therefore fail to capture the economic dependence of actual PDs [see e.g. Gordy & Howells, 2004; Heitfield, 2005].
This distinction clarifies that TTC rating processes are not “cycle-free” per se, but rather isolate cyclicality in default behaviour rather than in rating migrations.
4. Stylised illustration
A stylised firm-value example, following the tradition of structural credit risk models [Merton, 1974], illustrates how PIT and TTC ratings evolve along the same economic path. PIT ratings respond strongly to economic changes, while TTC ratings remain comparatively stable. Defaults occur under both approaches, but their attribution to rating grades differs systematically.
The example highlights how TTC ratings can be constructed to remain consistent with PIT information over longer horizons, a property that is often required in internal model governance.
Summary, conclusion, and outlook
For risk professionals, the key contribution of this framework lies in clarifying the structural relationship between economic conditions, rating migrations, and default probabilities. PIT and TTC ratings differ not merely in calibration, but in how and where macroeconomic information enters the rating system. Making this distinction explicit improves transparency, validation, and governance, particularly in institutions operating multiple PD concepts simultaneously.
The framework supports a consistent treatment of regulatory capital and expected loss modelling without relying on ad hoc PIT-to-TTC transformations. Looking ahead, economically conditioned rating models provide a natural foundation for macro stress testing, climate-related scenario analysis, and forward-looking risk assessment. As supervisory expectations increasingly emphasise coherence and explainability across credit risk models, unified approaches of this type are likely to gain further relevance.
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Link to the paper: http://doi.org/10.1002/cjs.70039