Mod-Poisson approximation schemes: Applications to credit risk

TL;DR

This paper presents a new numerical approximation method for credit portfolio models based on mod-$$ convergence, improving accuracy and efficiency over existing methods in risk measure estimation and tranche pricing.

Contribution

It introduces a novel correction-based approximation scheme leveraging mod-$$ convergence, enhancing accuracy and computational efficiency in credit risk calculations.

Findings

The method outperforms recursive, large deviations, Chen–Stein, and Monte Carlo methods in accuracy.

It requires less computational time than traditional approaches.

The approach provides better risk measure estimates and tranche prices.

Abstract

We introduce a new numerical approximation method for functionals of factor credit portfolio models based on the theory of mod-$\phi$ convergence and mod-$\phi$ 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.