Equity Option Implied Probability of Default and Equity Recovery Rate

Abstract

There is a close link between prices of equity options and the default probability of a firm. We show that in the presence of positive expected equity recovery, standard methods that assume zero equity recovery at default misestimate the option‐implied default probability. We introduce a simple method to detect stocks with positive expected equity recovery by examining option prices and propose a method to extract the default probability from option prices that allows for positive equity recovery. We demonstrate possible applications of our methodology with examples that include financial institutions in the United States during the 2007–09 subprime crisis. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:599–613, 2017

What do we know about individual equity options?

“…They show that the implied probabilities of default extracted from out-of-the-money puts closely match those embedded in CDS spreads. Chang and Orosi (2016) extend their modeling assumption by incorporating a positive expected equity recovery into the framework. They show that this adjustment results in a more accurate estimation of the implied probability of default using options on individual stocks.…”

Leveraging prices from credit and equity option markets for portfolio risk management

“…Therefore our contributions are threefold. First, we expand on the idea of Carr and Wu (2011) and Chang and Orosi (2017, 2020) by using URCs in a novel application—in concert with CDS premiums—to extract both default intensities and recovery rates, thus circumventing the identification problem mentioned above. Unlike many studies in the literature, using two derivatives from two different markets allows us to disentangle the changes in the default intensities from those in the recovery rates.…”

“…The URC is thus directly related to the default probability. Other default probability extraction techniques based on option prices have been recently proposed by Taylor et al (2014), Le (2015), Chang and Orosi (2017, 2020), and Conrad et al (2020).…”

“…New extraction methodologies based on option prices have been recently proposed in the literature. For instance,Chang and Orosi (2017) proposed an extraction method for default probabilities that allows for positive equity recovery; this assumption is different thanCarr and Wu's (2011), which assume zero equity recovery Chang and Orosi (2020). used a similar argument toCarr and Wu (2011) to extract default probabilities; instead of relying only on one deep out-of-the-money option, however, they proposed a method that can use more than one option price.…”