混合跳-扩散模型下一类基金公司的金融债券定价与违约概率研究

Pricing of Fund Corporate Bonds and Default Probability Study under Mixed Jump-diffusion Model

利用结构化方法构造了一类基金公司的金融债券组合,采用求解随机偏微分方程的方法,推导出混合跳-扩散模型下的债券定价公式,给出了基金公司在短期债券存续期间没有违约的概率和基金公司资产的条件分布,得到了基金公司金融债券组合的定价公式和违约概率的显式表达式,最后通过一个算例来分析模型的不同参数对基金公司债券价格以及违约概率的影响。结果表明,模型参数对短期债券的价格影响较大,短期债务的违约概率随着模型的Hurst参数H的增大而增加,并且风险系数变大时违约概率升高,在基金公司总债务不变的前提下,短期债务的权重大于中长期债务的权重时,公司的违约概率会变大。

By applying the structural approach, this paper studies a pricing model for internet financial bonds portfolio. By using the stochastic partial differential equations methods, the probability of no default before the short term bond maturity and the conditional distribution of the fund corporate assets is obtained under the mixed jump-diffusion fractional Brownian motion environment, and the pricing formula for both the short term and long term bond are derived. In the end, some numerical examples are given to illustrate the influence of different parameters to the short term bond prices and default probability of the fund corporate. It is shown that the different parameters will greatly affect the prices of short-term bonds. The default probability of short-term debt increases with the increase of the Hurst parameter of the model, and the probability of default increases when the risk factor becomes larger. Under the premise that the total debt of the fund corporate remains unchanged, when the weight of short-term debt is greater than the weight of medium-term and long-term debt, the corporate^s probability of default will increase.