Extracting Option-Implied Probability of Default: A Novel Method

Abstract

In this paper, we present a novel method to extract the risk-neutral probability of default from American put option prices. Under the assumptions of Carr and Wu (2011), we derive a closed form expression for American put options from which the probability of default can be inferred. Our empirical results based on four large institutions in the US during the 2007-2009 crisis show that directly applying the methodology of Carr and Wu (2011) can overestimate the probability of default. Our model also allows us to test the effect of positive equity recovery on estimated default probabilities.

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

JEL Classification: G01, G12, G13, G14