A Structural Model for the Fair Valuation of CDS Index Tranches
37 Pages Posted: 14 Feb 2018
Date Written: January 30, 2018
Abstract
We present a Monte Carlo valuation of iTraxx IG index tranches, combining structural and reduced-form models. The aim is to find tranche fair values, taking into account full term structures and actual correlations between individual firms.
For 125 firms in the index, 1, 3 and 5-year CDS are used to calibrate term structure parameters: initial asset/debt ratio, asset volatility, and Poisson jump-to-default intensity. Dependency is introduced using a 125x125 equity return correlation matrix, and used to value 0-3%, 3-6%, 6-9%, 9-12%, 12-22% and 22-100% tranches. Initial results overestimate the mezzanine versus equity tranches. In addition, heterogeneity in correlations and CDS has little impact on the equity-to-mezzanine ratio.
We demonstrate two extensions towards more realistic pricing: i) a two-correlation approach that allows asset value correlations to differ from jump-time correlations, and ii) allowing random correlations in both asset values and jumps.
To our knowledge, this is the first study to calibrate individual CDS term structures and use the parameters in combination with historical or random correlation estimates to price tranches. It provides a framework for combining empirical and market-implied data to value potentially illiquid products.
Keywords: CDS, CDO, Structural Model, Credit Risk, Copula
JEL Classification: C63, G13
Suggested Citation: Suggested Citation