A Simple Method for Extracting the Probability of Default from American Put Option Prices
A put option is a financial contract that gives the holder the right to sell an asset at a specific price by (or at) a specific date. A put option can therefore provide its holder insurance against a large drop in the stock price. This makes the prices of put options an ideal source of information for a market-based measure of the probability of a firm’s default.
We develop a simple method for estimating the probability that a firm will default based on the prices of its put option contracts. We first develop a simple closed-form pricing formula for American-style put options, incorporating the possibility of default. We then adjust the parameters of the proposed pricing formula to match observed put option prices to estimate the probability of a firm’s default. We test our method by using data on seven US firms (Altria, AT&T, Citigroup, Fannie Mae, Ford, General Motors and IBM) for the period 2002 to 2010.
The probabilities of default based on stock option prices show similar trends to the estimates implied by their credit default swaps (CDS). However, we find that the two measures can be significantly different in some cases. For instance, our analysis of these companies during the 2007–09 financial crisis indicates that, in some cases, the probability of default implied by their CDS may have been either too low (Fannie Mae) or too high (Ford). These results show that our estimates based on options complement the estimates based on CDS-spreads.