Implied Multi-Factor Model for Bespoke CDO Tranches and other Portfolio Credit Derivatives

TL;DR

This paper presents a semi-parametric, multi-factor model for pricing and managing bespoke CDO tranches, leveraging a prior index model and reweighting via Minimum Cross Entropy for computational efficiency.

Contribution

It introduces a novel approach combining a fixed prior model with reweighting to accurately price bespoke CDO tranches without extensive calibration.

Findings

Efficient convex optimization for model calibration.

Applicable to static and dynamic pricing of complex credit derivatives.

Enables risk management and CVA calculation for bespoke portfolios.

Abstract

This paper introduces a new semi-parametric approach to the pricing and risk management of bespoke CDO tranches, with a particular attention to bespokes that need to be mapped onto more than one reference portfolio. The only user input in our framework is a multi-factor model (a "prior" model hereafter) for index portfolios, such as CDX.NA.IG or iTraxx Europe, that are chosen as benchmark securities for the pricing of a given bespoke CDO. Parameters of the prior model are fixed, and not tuned to match prices of benchmark index tranches. Instead, our calibration procedure amounts to a proper reweightening of the prior measure using the Minimum Cross Entropy method. As the latter problem reduces to convex optimization in a low dimensional space, our model is computationally efficient. Both the static (one-period) and dynamic versions of the model are presented. The latter can be used for pricing and risk management of more exotic instruments referencing bespoke portfolios, such as forward-starting tranches or tranche options, and for calculation of credit valuation adjustment (CVA) for bespoke tranches.