Jump-diffusion Model-based Study on Dividend Distribution and Bankruptcy of Companies

Abstract:

This research examines the valuation of companies incorporating dividend payments and default risk under the Merton jump-diffusion framework. By integrating Girsanov’s measure transformation theory with probabilistic methodologies， we derive analytical solutions for three pivotal metrics： the present enterprise value， survival probability， and discounted dividend value. Numerical experiments are conducted to validate the analytical solutions， with results benchmarked against Monte Carlo simulations， confirming both the accuracy and computational efficiency of the proposed approach. Furthermore， the methodology demonstrates extensibility to the pricing of exotic structured derivatives， particularly double-barrier snowball options and shark-fin instruments requiring dual-threshold modeling.