Paper: arXiv 2509.10586

Authors: Vahab Rostampour

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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical foundation using control theory and state-space mechanics to solve a common practitioner problem in IFRS 9/CECL credit risk modeling. While the empirical validation relies on a synthetic corporate portfolio rather than extensive historical datasets, the mathematical rigor and novelty of the anchored Kalman filter approach are substantial.

Research Flowchart

  flowchart TD
    A[Research Goal: Stabilize Lifetime PD Models under Forecast Uncertainty] --> B[Input: Macroeconomic Forecasts & Synthetic Corporate Portfolio]
    B --> C[Formulate State-Space Model for PD Term Structures]
    C --> D[Evaluate Direct Kalman Filter: Finds Non-Vanishing Volatility]
    D --> E[Introduce Anchored Observation Model with Neutral Long-Run State]
    E --> F[Prove Asymptotic Stochastic Stability & Run Simulations]
    F --> G[Outcome: Reduced Noise, Smooth & Interpretable Lifetime PD Projections]

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0 of 46 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.