Early exercise decision in American options with dividends, stochastic volatility and jumps

TL;DR

This paper uses a fast numerical method to analyze early exercise decisions in American options on dividend-paying stocks, highlighting the importance of accurate dividend modeling and the impact of stochastic volatility and jumps on investor suboptimal exercise.

Contribution

It demonstrates that incorporating stochastic volatility and jumps significantly improves the accuracy of American option pricing and early exercise boundary estimation.

Findings

Correct modeling of dividends is crucial for accurate early exercise boundary calculation.

Stochastic volatility and jumps reduce suboptimal exercise losses by 25%.

Remaining losses may be due to monitoring costs rather than transaction fees.

Abstract

Using a fast numerical technique, we investigate a large database of investor suboptimal non-exercise 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.