Paper: arXiv 2505.13822

Authors: Masato Hisakado, Shintaro Mori

Abstract

This study considers the Merton model with temporal correlation. We show the Merton model becomes Poisson process with the log-normal distributed intensity function in the limit. We discuss the relation between this model and Hawkes process. In this model we confirm the super-normal transition when the temporal correlation is power case. The phase transition is same as seen before the limit. We apply this model to the default portfolios and find that the power decay model provides better generalization performance for the long term data.

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 rigorous mathematical derivation linking the Merton credit risk model with temporal correlation to a Poisson process with log-normal intensity and Hawkes processes. While it establishes solid theoretical bounds for phase transitions under power-law correlation decay, the empirical backtesting section is concise and primarily illustrative.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Merton Model with Temporal Correlation] --> B[Theoretical Limit Derivation]
    B --> C[Poisson Process with Log-Normal Intensity & Hawkes Link]
    C --> D[Evaluate Temporal Correlation: Power Decay vs Exponential]
    D --> E[Input: Default Portfolios Long-Term Data]
    E --> F[Empirical Validation & Generalization Testing]
    F --> G[Outcomes: Super-Normal Phase Transition Confirmed & Power Decay Performs Best]

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0 of 13 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.