CDS and equity volatility: theoretical modelling and …_Giorgio CONSIGLI CREDIT DEFAULT SWAPS AND EQUITY VOLATILITY: THEORETICAL MODELLING AND MARKET EVIDENCE Giorgio CONSIGLI E-mail: giorgio@giorgioconsigli.it DMSIA Università di Bergamo and UniCredit Banca Mobiliare ABSTRACT - The joint behaviour of equity premiums and credit spreads on securities is- sued by the same company provides a direct statistical evidence of the degree of efficiency of equity and fixed income markets, whose participants are expected in the long term to provide a common risk assessment. Increasing interest in the financial industry is attracted both for financial engineering and trading purposes, by the potentials offered by contracts with equity and fixed income compo- nents. Increased liquidity in the credit default swaps (CDS) market, on the other hand, provides new grounds for fixed income analysis based on the statistical study of theoretical versus actual spread movements. In the paper we analyse the statistical relationship between CDS spreads, stocks implied volatility and theoretical spreads generated by an application of Merton seminal structural default model. A measure of price discrepancies is also proposed, based on the difference between theoretical and actual spread behaviours, leading to an application of relative value analysis in the fixed income market. We also test the dependence of credit spreads behaviour on the volatility of the associated equity returns and the relationship over time between theoretical and observed CDS spreads. The analysis is applied to six large corporations and back-tested over the 2002-2003 period. Ford and General Motors are considered for the sector of Automotives, Deutsche Telekom and France Telecom for Telecommunications, Endesa and RWE for the sector of Utilities. We show that implied volatility movements drive significant spread movements: both theo- retical and actual spreads follow volatility patterns. Furthermore, the impact on the theoreti- cal spreads provides an accurate proxy of forthcoming movements in actual spreads. This general results applies in particular to companies with a sufficient degree of risk (i.e. lever- age), while poor evidence can be collected for companies relatively free of default risk. KEYWORDS – Credit risk, Structural default model, Relative value analysis, Credit default swaps, implied volatility.