Bankruptcy probabilities inferred from option prices

Stephen J. Taylor, Chi Feng Tzeng, Martin Widdicks

Research output: Contribution to journalArticlepeer-review


In times of financial crisis, solvency concerns are reflected in market prices for financial instruments. Credit default swap (CDS) spreads provide a direct measure of the market's (risk-neutral) expectation regarding a firm's probability of bankruptcy. The options market is another place where investors' projections of future credit conditions can be seen, in high prices for deep out-of-the-money puts, for example. Although CDS spreads are available for horizons of 1 to 10 years and more, option maturities are much shorter, offering a window onto short-term expec-tations. Moreover, unlike CDS, the availability of market prices for multiple options with the same expiration but different strike prices allows an entire risk-neutral density (RND) for the future stock price to be extracted. In this article, the authors extend the strategy of fitting the RND as a mixture of two lognormals by adding a discrete probability of bankruptcy. Applying the approach to analyze the RNDs from equity options on Bear Stearns, Lehman, Merrill Lynch, and AIG in the run-up to their 2008 credit events (two of which ended in forced mergers and the other two in insolvency), the authors find that the mixture of lognormals plus bankruptcy RND fits the options market data better than alternative models. They also show that the implied short-run bankruptcy probabilities from equity options aligned perfectly with the one-year CDS spreads and also that the RND default probabilities for J.P. Morgan and Bank of America, which took over the failing Bear Stearns and Merrill Lynch, respectively, were much lower than for the four firms that experienced credit events.

Original languageEnglish (US)
Pages (from-to)8-31
Number of pages24
JournalJournal of Derivatives
Issue number2
StatePublished - Dec 1 2014

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics


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