Equity Option Implied Probability of Default and Equity Recovery Rate

Abstract

There is a close link between prices of equity options and the probability of default of a firm. We show that in the presence of positive expected equity recovery, the standard methods that assume zero equity recovery at default misestimate the probability of default implicit in option prices. We introduce a simple method to detect stocks with positive expected equity recovery by examining option prices, and propose a method to extract the probability of default from option prices in the presence of positive expected equity recovery. Our empirical results based on six large financial institutions in the US during the 2007-2009 crisis show that assuming zero recovery leads to significant mispricing of options and misestimation of implied probability of default.