Structural credit risk model driven by Lévy process under knight uncertainty

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.