论文标题
Mod-Poisson近似计划：申请信用风险
Mod-Poisson approximation schemes: Applications to credit risk
论文作者
论文摘要
我们基于mod-$ $ ϕ $收敛性和mod- $ n $近似方案的理论，为因素信用组合模型的功能引入了一种新的数值近似方法。该方法可以理解为为经典的泊松近似提供校正项，其中高阶校正会导致渐近近似值随着债务数量的增加而近似近似。我们对两个任务进行经验测试：风险度量的估计（$ \ MATHRM {var} $和$ \ Mathrm {es} $）和CDO Tranche价格的计算。我们将其与其他常用方法（例如递归方法，较大的偏差近似，Chen-stein方法和蒙特卡洛模拟技术（有或没有重要性采样））进行比较 - 我们证明它会导致更准确的估计值，同时需要较少的计算时间。
We introduce a new numerical approximation method for functionals of factor credit portfolio models based on the theory of mod-$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.
