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Structural credit risk model driven by Lévy process under knight uncertainty.

Zhenyu Tang1, Bin Zhong1, Liang Zhou2

  • 1Gannan University of science and technology, Jiangxi University of science and technology, Ganzhou, 341000 JiangXi China.

Annals of Operations Research
|June 26, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new credit risk model accounting for Knight Uncertainty, moving beyond traditional geometric Brownian motion. It provides a dynamic pricing framework for default and stock values in Lévy markets.

Keywords:
Knight uncertaintyLévy processNumerical analysisStructural credit risk model

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Area of Science:

  • Quantitative Finance
  • Financial Risk Management

Background:

  • Conventional credit risk models assume risky asset values follow geometric Brownian motion.
  • Real-world asset values exhibit non-continuous, jump-diffusion behavior, making Knight Uncertainty difficult to quantify with single probability measures.

Purpose of the Study:

  • To analyze a structural credit risk model within a Lévy market framework incorporating Knight Uncertainty.
  • To develop a dynamic pricing model for default probability, stock value, and bond value under these conditions.

Main Methods:

  • Utilized the Lévy-Laplace exponent to construct a dynamic pricing model.
  • Derived explicit solutions for value processes assuming a log-normal distribution for the jump process.

Main Results:

  • Established price intervals for default probability, stock value, and bond value.
  • Numerical analysis demonstrated the significant impact of Knight Uncertainty on pricing default and stock values.

Conclusions:

  • The proposed Lévy market model effectively incorporates Knight Uncertainty into credit risk pricing.
  • Findings highlight the necessity of accounting for non-continuous asset dynamics and Knight Uncertainty for accurate financial market valuation.