Equity Option Implied Probability of Default and Equity Recovery Rate

A Simple Method for Extracting the Probability of Default from American Put Option Prices

“…This limitation is clearly demonstrated in <Figure 1>, where we plot the daily prices of each stock in our sample, together with the daily lowest put strike price available. We …nd that with the exception of Ford, most stocks do not have the deep-out-of-the-money puts (e.g., strikes of less than $5 as in CW) that are required to estimate the probability of default when using the formula in equation (5). However, our problem presents an additional challenge that is inherent in applying this general approach because the problem requires more robustness in its extrapolation beyond the lowest available strike, compared to other problems where it is su¢ cient to make a reasonable interpolation within the available strikes.…”

“…They …nd that employing European-style options to estimate PD is superior to the Moody's KMV model (Bohn et al, 2005) and other popular approaches. Chang and Orosi (2017) also develop a methodology for extracting the default probability from the prices of low-strike in-the-money call options.…”

A robust method to retrieve option implied risk neutral densities for defaultable assets

“…In this section, we consider the case when the value of the stock in the case of default is given by  a non-zero value. Moreover, Chang and Orosi (2016) show that…”

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 () 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.…”