Using a fast numerical technique, we investigate a large database of investor suboptimal nonexercise of short maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modelling of the discrete dividend is essential for a correct calculation of the early exercise boundary as confirmed by theoretical insights. Pricing with stochastic volatility and jumps instead of the Black-Scholes-Merton benchmark cuts by a quarter the amount lost by investors through suboptimal exercise. The remaining three quarters are largely unexplained by transaction fees and may be interpreted as an opportunity cost for the investors to monitor optimal exercise.