跳扩散模型下公司的红利分配和破产问题研究

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

摘要:

在Merton跳扩散模型下研究了带有红利支付和违约特征的公司的相关计算问题。基于Girsanov测度变换理论，使用概率论方法，推导出了公司的价值现值、生存概率和股利现值的解析解。最后进行了数值试验，并与蒙特卡罗模拟的数值结果进行了比较，验证了推导出的解析解的正确性与高效性。所提出的方法可以进一步推广到带有双障碍特点的雪球期权及鲨鱼鳍型衍生品的定价问题研究。

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.