Simple Robust Linkages between CDS and Equity Options

Abstract

We test a theory that provides a simple and robust link between market prices of credit default swaps (CDS) and equity options. The theory links the CDS spread to the market prices of vertical spreads of American put options which are sufficiently out-of-the-money. T he linkage is established under a general class of stock price dynamics for which the default event affects only the state space in which stock prices evolve. Specifically, stock prices are assumed to be bounded below by a barrier B > 0 strictly before the default event, and to drop below an alternative barrier A < B at the default time. We allow random stock price evolution after default, so long as it is bounded above by A. We suppose that investors can take a static position in at least two co-terminal American put options struck within the 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 above state space behavior, we show that this simple replicating strategy is robust to the details of the pre-default stock price dynamics, the post-d efault stock price dynamics, interest rate dynamics, and default arrival rate fluctuations. We use the value of the American put spread to infer risk-neutral default probabilities and compare them to the default probabilities estimated from CDS spreads on the same reference company. Collecting data from both markets on several reference companies with significant default probabilities, we identify a strong correlation between the defa ult probabilities inferred from the two markets, and find that deviations between the two estimates help predict f uture movements in both markets.