Stabilising Lifetime PD Models under Forecast Uncertainty

2025/09/12 by Vahab Rostampour, Rostampour, Vahab
Decision Sciences · Economics, Econometrics and Finance · #Capital Investment and Risk Analysis #FOS: Economics and business #FOS: Electrical engineering #Forecasting Techniques and Applications #Monetary Policy and Economic Impact #Risk Management (q-fin.RM) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2509.10586

openalex publication_date 2025/09/12 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

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.

Citations

• Sensitivity and convergence of uniformly ergodic Markov chains
• A real-time data set for macroeconomists
• Trends and random walks in macroeconmic time series

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