Simple robust linkages between CDS and equity options

Liuren Wu (Baruch College)

We develop a simple robust linkage between credit default swaps (CDS) and
American put stock options on the same reference company. Assuming that the
stock price stays above a barrier B before default but drops and remains below a lower barrier A<B after default, we show that the spread between two co-terminal American put options struck within the default corridor [A,B] scaled by their strike
difference replicates a standardized credit insurance contract that pays one dollar at default whenever the company defaults prior to the option expiry and zero otherwise. As long as the default corridor exists, 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 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.