A Joint Analysis of the Term Structure of Credit Default Swap Spreads and the Implied Volatility Surface

Abstract

This paper presents a joint analysis of the term structure of credit default swap (CDS) spreads and the implied volatility surface. The rapid development of the CDS market has provided convenient products to extract credit risk, and its interaction with equity volatility has been analyzed in many studies. However, in most of them the 5-year credit default swap spread is used to measure credit risk, whilst the at-the-money 1-month implied volatility is used to measure equity volatility. Only very few studies analyze the entire smile and the term structure of CDS spreads.

The purpose of this paper is to study the co-movements of the term structure of credit default swap spreads and the implied volatility surface. We perform a factor decomposition for both the dynamics of the implied volatility surface and the CDS curve. Then we jointly analyze the factors. More precisely, we compute the information flow between the credit and volatility factors, scrutinize the contemporaneous interactions between the factors, and study the efficiency of cross-hedges between the credit and volatility markets.

Using time series of options and CDS curves for the U.S. and European markets, we find that the credit market is the main contributor to overall market innovations. Our methodology is parsimonious and allows to capture the intrinsic relationships between the two markets. The empirical study highlights the existing cross-market linkages during the Global Financial Crisis. It also underlines that factors with small associated eigenvalues can be of tremendous importance to perform efficient cross-hedges.

Keywords: Credit Default Swap, Term Structure, Implied Volatility Surface, Factor Decomposition, Information Flow, Market Linkages, Cross-Hedging

JEL Classification: C14, C58, G12, G13