Exact Pricing Asymptotics for Investment-Grade Tranches of Synthetic CDO's. Part II: A Large Heterogeneous Pool

TL;DR

This paper applies large deviations theory to accurately analyze the pricing of investment-grade tranches in large, heterogeneous synthetic CDO pools, accounting for complex correlations and idiosyncratic risks.

Contribution

It extends large deviations analysis to heterogeneous pools, providing precise asymptotic pricing formulas for synthetic CDO tranches with general correlation structures.

Findings

Precise asymptotic pricing formulas derived for heterogeneous pools.

Effective handling of complex correlation structures.

Enhanced understanding of risk behavior in large CDO portfolios.

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 heterogeneous pool of names. Our main tool is a large-deviations analysis which allows us to precisely study the behavior of a large amount of idiosyncratic randomness. Our calculations allow a fairly general treatment of correlation.