Paper: arXiv 2409.09179

Authors: Mohamed Ben Alaya, Ahmed Kebaier, Djibril Sarr

Abstract

This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily addresses two gaps in the literature. The first is the lack of credit spread models founded on a stochastic basis that enables continuous modeling, as many existing models rely on factorial assumptions. The second is the limited availability of models that directly yield a term structure of credit spreads. An intermediate result of our model is the provision of a term structure for the prices of defaultable bonds. We present the model alongside an innovative, practical, and conservative calibration approach that minimizes the error between historical and theoretical volatilities of default intensities. We demonstrate the robustness of both the model and its calibration process by comparing its behavior to historical credit spread values. Our findings indicate that the model not only produces realistic credit spread term structure curves but also exhibits consistent diffusion over time. Additionally, the model accurately fits the initial term structure of implied survival probabilities and provides an analytical expression for the credit spread of any given maturity at any future time.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical derivation for pricing defaultable bonds and credit spreads using a CIR++ intensity framework. It addresses a real market gap by providing closed-form solutions and practical calibration techniques, accompanied by historical backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Continuous Stochastic Modeling of Credit Spread Term Structure] --> B[Inputs: Historical Credit Spreads & Default Intensities]
    B --> C[Framework: CIR++ Model for Default Intensity Diffusion]
    C --> D[Model Formulation: Derivation of Defaultable Bond Prices & Survival Probabilities]
    D --> E[Calibration: Minimized Volatility Error Between Theoretical & Historical Data]
    E --> F[Outcomes: Analytical Expression for Credit Spreads & Realistic Term Structure Dynamics]

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0 of 61 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.