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

Abstract

In this paper, we present a novel method to extract the risk-neutral probability of default of a from from American put option prices. Building on the idea of a default corridor proposed in Carr and Wu (2011), we derive a parsimonious closed-form formula for American put option price from which the probability of default can be inferred. The proposed method is easy to implement and helps overcome the main limitation of the method used in Carr and Wu (2011), which relies on the price of one deep-out-of-the-money put option. Our empirical results based on seven large U.S. firms between 2002 and 2010 show that the option-implied probability of default can provide a more accurate estimate of default probability in some cases, compared to the estimates implied from credit default swap spreads.

Keywords: default, probability of default, American put option, arbitrage, lower bounds

JEL Classification: G01, G12, G13, G14