Options on Troubled Stock

This study uses equilibrium arguments to derive closed‐form solutions for the price of European call and put options written on an individual stock when shareholders might lose all their claims on the firm. The stock price accounts for both a random probability of bankruptcy and a random probability of remaining a going concern. With a random probability of bankruptcy, shareholders lose all their claims in the firm. With a random probability of remaining a going concern, the stock price is lognormal as in the Black–Scholes model. The bankruptcy probability is correlated with aggregated wealth if the bankruptcy risk is systematic. The model is consistent with a bankruptcy probability negatively correlated with the firm's stock price. If the bankruptcy probability of a given firm increases then its stock price decreases which leads to the value of the call options written on that stock to decrease. This result is not obtainable under Merton's (1976) ruin model where the stock price and the bankruptcy probability are independent. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:637–657, 2014