A simple method for extracting the probability of default from American put option prices

Abstract

We present a novel method for extracting the risk‐neutral probability of default (PD) of a firm from American put option prices. Building on the idea of a default corridor proposed by Carr and Wu, we derive a parsimonious closed‐form formula for American put option prices from which the PD can be inferred. The method is easy to implement. Our empirical results based on seven large US firms for the period 2002–2010 show that, in some cases, our option‐implied PD can provide a more accurate estimate of default probability than the estimates implied from credit default swaps.

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

“…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).…”

“…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.…”

“…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.…”