Modeling Fuzzy Moral Hazard in Credit Default Swap Pricing: A Reduced-Form Approach

In existing literature, moral hazard is often modeled as a constant. However, moral hazard can be “fuzzy” rather than “precisely defined.” As moral hazard is dynamic and variable, exhibiting both constancy and differentiation, its representation through fuzzy intervals—rather than fixed constants—has emerged as a meaningful research direction. This paper integrates fuzzy set theory into credit default analysis, combining moral hazard, fuzzy risk, and credit risk in a cross-disciplinary study to explore their intrinsic interdependencies. First, a novel default intensity model incorporating market state variables and moral hazard state variables is proposed. By accounting for the fuzzy risks inherent in trading environments, the moral hazard indicators are transformed into fuzzy intervals, thereby establishing interval-based moral hazard metrics to characterize default intensity. Subsequently, to address the phenomenon of default clustering caused by default dependence in markets, a circular default intensity model involving two reference assets is constructed. Within this framework, the cross-influence mechanisms of moral hazard and fuzzy risk are further investigated. Furthermore, the proposed model, which integrates moral hazard and fuzzy risk, is applied to derivative pricing. A new pricing formula for default management costs is derived. Finally, through comparative analysis and simulation experiments, the study concludes that: (1) Under the parameter settings representing economic stagnation, the triangular fuzzy interval of survival probability narrows progressively as the credibility parameter $$\gamma$$ increases, eventually converging to a real number. (2) The cost of credit default management is significantly influenced by the number of reference assets. In trading environments where moral hazard, fuzzy risk, and credit risk intertwine, effective mitigation of their impacts on default risk requires strategic information utilization and reduction in the number of reference assets. This approach not only lowers credit management costs but also fosters the healthy development of financial markets.