Option Prices and the Probability of Success of Cash Mergers

When a cash merger is announced but not yet completed, there are two key unobserved variables involved in the target company stock price: the probability of success, and the fallback price, i.e., the price conditional on merger failure. We propose an arbitrage-free model involving these two sources of uncertainty which prices European options on the target company. We empirically test our formula in a study of all cash mergers between 1996 and 2008. The formula matches well the observed volatility smile. Furthermore, as predicted by the model, we show empirically that the volatility smile displays a kink, and that the kink is proportional to the risk-neutral probability of deal success. JEL Classification: G13, G34.