Stabilising Lifetime PD Models under Forecast Uncertainty
lifetime PD, point-in-time PD, macroeconomic scenarios, forecast error propagation, anchored observation model, stochastic stability, convergence in probability, procyclicality, Monte Carlo simulation, transition-matrix projection
Abstract
Estimating lifetime probabilities of default (PDs) under IFRS9 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.
Anchored state-space approach for stable lifetime PD; less drift, less procyclicality. Code and full reproducibility.
Materials
- Source paper: https://github.com/vahabr/research-lab/tree/main/lifetime-PD-AKF/paper
- Code & notebooks: https://github.com/vahabr/research-lab/tree/main/lifetime-PD-AKF/code
- Repro bundle (.zip): https://github.com/vahabr/research-lab/tree/main/lifetime-PD-AKF/code/kalman_pd_simulation_bundle.zip
- Environment:
anchored-kf.qmd
/requirements.txt
- arXiv preprint: http://arxiv.org/abs/2509.10586
How to cite
Rostampour, V. (2025). Stabilising Lifetime PD Models under Forecast Uncertainty. arXiv:XXXXXXXX.
@misc{rostampour2025akf,
title = {Stabilising Lifetime PD Models under Forecast Uncertainty},
author = {Rostampour, Vahab},
year = {2025},
eprint = {http://arxiv.org/abs/2509.10586},
archivePrefix= {arXiv},
primaryClass = {q-fin.RM}
}