基于时变布朗运动的信用风险建模
Credit risk modeling using time-changed Brownian motion
摘要：
出于结构和简化形式的信用模型之间的相互作用，我们建议模型的企业价值过程作为一个随时间变化的布朗运动，可能包括跳跃和随机波动率的影响，并研究这种过程的第一通道问题。我们考虑修改随机过程的标准第一通道问题，以利用这种时间变化结构，并发现这种“第二类第一通道时间”的分布函数在广泛的有用的例子是有效的计算。因此，这个新的概念的第一通道可以用来定义广义结构信用模型的违约时间。给出了可违约债券和信用违约互换的计算公式，这些公式既可有效计算，又能得到真实的利差曲线。最后，我们表明，通过处理联合企业价值过程的独立的布朗运动的依赖时间变化，可以得到多企业信用模型与丰富的和合理的动态和享受有效的组合信用衍生品的估值的可能性。
英文摘要：
Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider modifying the standard first passage problem for stochastic processes to capitalize on this time change structure and find that the distribution functions of such "first passage times of the second kind" are efficiently computable in a wide range of useful examples. Thus this new notion of first passage can be used to define the time of default in generalized structural credit models. Formulas for defaultable bonds and credit default swaps are given that are both efficiently computable and lead to realistic spread curves. Finally, we show that by treating joint firm value processes as dependent time changes of independent Brownian motions, one can obtain multifirm credit models with rich and plausible dynamics and enjoying the possibility of efficient valuation of portfolio credit derivatives.
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