Stabilising Lifetime PD Models under Forecast Uncertainty

Vahab Rostampour

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arXiv · 2509.10586

Stabilising Lifetime PD Models under Forecast Uncertainty

Vahab Rostampour

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Abstract

Estimating lifetime probabilities of default (PDs) under IFRS~9 and CECL requires projecting point--in--time transition matrices over multiple years. A persistent weakness is that macroeconomic forecast errors compound across horizons, producing unstable and volatile PD term structures. This paper reformulates the problem in a state--space framework and shows that a direct Kalman filter leaves non--vanishing variability. We then introduce an anchored observation model, which incorporates a neutral long--run economic state into the filter. The resulting error dynamics exhibit asymptotic stochastic stability, ensuring convergence in probability of the lifetime PD term structure. Simulation on a synthetic corporate portfolio confirms that anchoring reduces forecast noise and delivers smoother, more interpretable projections.

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Vahab Rostampour. 2025-09-12. Stabilising Lifetime PD Models under Forecast Uncertainty. https://arxiv.org/abs/2509.10586

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