Mod-Poisson逼近格式在信用风险中的应用
Mod-Poisson approximation schemes: Applications to credit risk
摘要：
基于mod- $ϕ$收敛性理论和mod- $ϕ$逼近格式，给出了因子信用组合模型泛函的一种新的数值逼近方法.该方法可以被理解为提供校正项的经典泊松近似，其中高阶校正导致渐近更好的近似的债务人的数量增加。我们在两个任务上对模型进行了实证测试：风险度量（$\mathrm{VaR}$和$\mathrm{ES}$）的估计和CDO份额价格的计算。我们比较它与其他常用的方法-如递归方法，大偏差近似，陈-斯坦方法和蒙特卡罗模拟技术（有和没有重要性抽样）-我们表明，它会导致更准确的估计，同时需要更少的计算时间。
英文摘要：
We introduce a new numerical approximation method for functionals of factor credit portfolio models based on the theory of mod-$ϕ$ convergence and mod-$ϕ$ approximation schemes. The method can be understood as providing correction terms to the classic Poisson approximation, where higher order corrections lead to asymptotically better approximations as the number of obligors increases. We test the model empirically on two tasks: the estimation of risk measures ($\mathrm{VaR}$ and $\mathrm{ES}$) and the computation of CDO tranche prices. We compare it to other commonly used methods -- such as the recursive method, the large deviations approximation, the Chen--Stein method and the Monte Carlo simulation technique (with and without importance sampling) -- and we show that it leads to more accurate estimates while requiring less computational time.
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