Unified pricing model for corporate stocks and bonds under bankruptcy reorganization observation period and discrete bankruptcy time

This paper investigates the impact of a finite bankruptcy reorganization observation period and discrete bankruptcy timing on corporate asset pricing and operational strategies. Discrete bankruptcy times are modeled by the jump moments of a Poisson process with intensity $\rho$, and a bankruptcy reorganization mechanism based on strategic debt payments is incorporated. Within the structural credit risk framework, the problem is formulated as a nonlinear optimal stopping problem with a penalty term. By employing Itô's lemma and partial differential equation methods, explicit analytical solutions for the values of corporate equity, debt, and firm value are derived, together with expressions for the optimal bankruptcy boundary and the optimal coupon level. Numerical results show that, compared with the continuous bankruptcy model, the discrete bankruptcy mechanism significantly increases the optimal bankruptcy boundary and the optimal coupon level. While the overall impact on firm value is relatively small, it substantially changes the distribution of value between equity and debt: Equity value decreases by approximately $6\mathrm{\%}$, whereas debt value increases by about $51\mathrm{\%}$. Furthermore, when the bankruptcy reorganization observation period extends from $0.5$ years to $1.5$ years, the divergence between equity and debt values becomes more pronounced. The proposed model provides theoretical insights for corporate bankruptcy reorganization strategies, capital structure optimization, and the pricing of corporate stocks and bonds under uncertain bankruptcy environments.