Option Pricing on Cash Mergers
Résumé
When a cash merger is announced but not completed, there are two main sources of uncertainty related to the target company: the probability of success and the price conditional on the deal failing. We propose an arbitrage-free option pricing formula that focuses on these sources of uncertainty. We test our formula in a study of all cash mergers between 1996 and 2008 which have sufficiently liquid options traded on the target company. The estimated success probability is a good predictor of the deal outcome. Our option formula for cash mergers does significantly better than the Black– Scholes formula and produces a volatility smile close to the one observed in practice. In particular, we provide an explanation for the kink in the volatility smile and show that the kink increases with the probability of deal success.