Simple Robust Linkages between CDS and Equity Options

Abstract

We test a theory that provides a simple and robust linkage between the market prices of credit default swaps (CDS) and far out-of-the-money equity American put options on the same reference company. The linkage is established under a general class of stock price dynamics. We assume that the stock price stays above a barrier B>0 before default but drops below a lower barrier A at default and stays blow A thereafter. We further assume that investors can take a static position in at least two American put options with the same expiry date and struck within this default corridor [A,B]. We show that a vertical spread of such options scaled by the spread between the two strikes replicates a standardized credit insurance contract that pays one dollar at default whenever the company defaults prior to the option expiry and zero otherwise. Given the existence of the default corridor, this simple replicating strategy is robust to the details of pre- and post-default stock price dynamics, interest rate movements, and default risk fluctuations. We use the American put spread to infer risk-neutral default probabilities and compare them to those estimated from the CDS spreads. Collecting CDS and American stock options data on several companies, we identify strong co-movements between the risk-neutral default probabilities inferred from the two markets. We also find that deviations between the two estimates predict future movements in both markets. In particular, the cross-market deviations predict future returns on the American put spread that synthesizes the credit insurance contract.

Keywords: Stock options, American puts, unit recovery claims, credit default swaps, default probabilities

JEL Classification: C13, C51, G12, G13