分数跳-扩散下信用风险中企业违约概率研究

Enterprise Default Probability of Credit Risk Under Fractional Jump-Diffusion Process

假定资产价值服从分数跳-扩散过程,利用分数布朗运动和跳过程的随机分析理论,得到了分数跳-扩散下的企业违约概率,并通过Matlab软件分析了主要参数对违约概率的影响:当影响资产价值变化的波动率σ固定时,随着泊松分布的参数λ和Hurst参数H的增大,违约概率逐渐变大,说明违约概率与这些参数密切相关。相比资产价值仅由分数布朗运动驱动,该模型更加符合实际。

Under the hypothesis that asset value obeys the fractional jump-diffusion process,the explicit formula of enterprise default probability of credit risk by the stochastic analysis theory for the fractional Brownian motion and jump process is obtained,and the influence of main parameters on default probability by Matlab simulation is analyzed.When asset value volatility σ is fixed,the default probability becomes more and more bigger,with the increasing of Poisson distribution parameter λ and Hurst parameter H,which indicates that the default probability is related to these parameters closely.Comparing to asset value being driven only by fractional Brownian motion,this model meets the truth further.