A Structural Credit Risk Model with Jumps Based on Uncertainty Theory

Hong Huang (), Meihua Jiang, Yufu Ning and Shuai Wang
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Hong Huang: School of Vocational Education, Shandong Youth University of Political Science, Jinan 250103, China
Meihua Jiang: School of Information Engineering, Shandong Management University, Jinan 250357, China
Yufu Ning: Key Laboratory of Intelligent Information Processing Technology and Security in Universities of Shandong, Jinan 250103, China
Shuai Wang: Key Laboratory of Intelligent Information Processing Technology and Security in Universities of Shandong, Jinan 250103, China

Mathematics, 2025, vol. 13, issue 6, 1-19

Abstract: This study, within the framework of uncertainty theory, employs an uncertain differential equation with jumps to model the asset value process of a company, establishing a structured model of uncertain credit risk that incorporates jumps. This model is applied to the pricing of two types of credit derivatives, yielding pricing formulas for corporate zero-coupon bonds and Credit Default Swap (CDS). Through numerical analysis, we examine the impact of asset value volatility and jump magnitude on corporate default uncertainty, as well as the influence of jump magnitude on the pricing of zero-coupon bonds and CDS. The results indicate that an increase in volatility levels significantly enhances default uncertainty, and an expansion in the magnitude of negative jumps not only directly elevates default risk but also leads to a significant increase in the value of zero-coupon bonds and the price of CDS through a risk premium adjustment mechanism. Therefore, when assessing corporate default risk and pricing credit derivatives, the disturbance of asset value jumps must be considered a crucial factor.

Keywords: structural credit risk model with jumps; default uncertainty; uncertainty theory; credit derivatives’ pricing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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