Credit Risk: Structural Models With Risk-Neutral Approach Under Uncertainty Theory

Credit risk, a critical component of financial risk management, concerns the possibility of borrower default. Traditional structural models, such as Merton’s framework, assume that firm asset values evolve according to stochastic differential equations driven by Brownian motion. However, real financial markets often exhibit ambiguity that cannot be captured by purely stochastic methods. In this work, we employ Liu’s uncertainty theory to construct a structural credit risk model based on belief degrees rather than probabilities. We develop an uncertain stock model for firm asset value and derive analytical expressions for the belief degree of default, expected returns, and the pricing of equity and debt. The model also accounts for balance sheet consistency, capital structure ratios, credit spread, partial recovery scenarios, and pricing under fixed asset values. Our results, supported by graphical illustrations, highlight the behavioral richness of credit markets under uncertainty and offer an alternative to classical stochastic approaches.