考虑作为风险因素的利率的跳跃,以研究信用衍生品的定价问题.通过影响信用衍生品参考债务实体违约概率相应的违约强度,利率的跳跃对信用衍生品的定价将产生影响.为此,令描述各个状态变量变化的随机过程是交叉激励的,以体现各事件之间的依赖关系.在线性一二次跳跃一扩散框架下给出了一般定价模型,并可通过Riccati方程组对其进行求解.最后,在特定的随机过程下,将所得定价模型应用在CDS上,并给出定价公式的显性表达式,以作举例.
In this paper, we study the valuation of credit derivatives with jumps in interest rates and propose a general pricing model under the linear-quadratic jump-diffusion framework. Jumps in interest rates would in- fluence intensities of default times, which decide the default possibilities that determine the prices of credit de- rivatives. We let the components of linear-quadratic process be cross-exciting and facilitate the description of complex event dependence structures. To illustrate how our model works, we make an application on CDS un- der the specific underlying processes, and an explicit formula of the fair CDS spread can be obtained through a system of matrix Riccati equations.