Statistical Modeling of Credit Default Swap Portfolios

Abstract

We undertake a systematic study of the univariate and multivariate properties of CDS spreads using the CDS spread time series of CDX Investment Grade index constituents from 2005 to 2009. We find that CDS spread returns appear to be stationary and exhibit positive autocorrelations, heteroscedasticity, two-sided heavy tails, serial dependence in extreme values, and large co-movements not necessarily linked to credit events. The first principal component of CDS spread returns corresponds to heavy-tailed parallel shifts in CDS spreads across obligors.

We then propose a heavy-tailed multivariate time series model for CDS spreads, which can be used as a framework for measuring and managing the risk of CDS portfolios. This model is shown to capture adequately the observed statistical properties of CDS spreads and has better performance than affine jump-diffusion or random walk models for predicting loss quantiles of various CDS portfolios. In particular, loss quantiles estimated using the heavy-tailed multivariate model adjust more rapidly to the market shocks in late 2008, with a consistent performance across normal and extreme market environments.

Keywords: credit default swaps, credit risk, stylized properties, risk management, autocorrelation, heavy tails, heteroscedasticity, principal component analysis, credit events, loss distribution, Value-at-Risk, expected shortfall, CDS

JEL Classification: C58 C51 G13 C32 G01