Valuation of a CDO and an n-th to Default CDS Without Monte Carlo Simulation

Abstract

Many of the new credit derivative products are based on default experience for a portfolio of financial instruments. These include collateralized debt obligations (CDOs) and similar tranched credit products, and “n-th to default swaps.” Devising good default risk models for single-name credits has been challenging enough, but applying them to credit portfolios introduces much greater complexity, because of the critical importance of correlation. The most common valuation technology is Monte Carlo simulation, but with many bonds, each of which is subject to both correlated and idiosyncratic risk factors, the simulation is time-consuming and limited in scope. In this article, Hull and White offer two straightforward approximation techniques for evaluating default risk within the industry-standard “copula“ model that eliminate simulation of the idiosyncratic risks. Their approach greatly accelerates the solution while still allowing a large degree of flexibility in the choice of factor correlation structure and probability distributions. For example, Student-t distributed shocks that have fatter tails than the normal are easily accommodated.