Exact Pricing Asymptotics of Investment-Grade Tranches of Synthetic CDO's Part I: A Large Homogeneous Pool

TL;DR

This paper applies large deviations theory to derive exact asymptotic pricing formulas for investment-grade tranches of synthetic CDOs in a simplified homogeneous pool model.

Contribution

It introduces a large deviations approach to derive precise asymptotic prices for CDO tranches, advancing quantitative risk modeling techniques.

Findings

Derived explicit large deviations-based pricing formulas

Provided insights into the tail risk of investment-grade tranches

Simplified model facilitates understanding of complex CDO pricing dynamics

Abstract

We use the theory of large deviations to study the pricing of investment-grade tranches of synthetic CDO's. In this paper, we consider a simplified model which will allow us to introduce some of the concepts and calculations.