American options with liquidation penalties

This paper integrates liquidation costs into the pricing of American options in an arbitrage-free and otherwise frictionless market. The introduction of liquidation penalties changes the comparison between immediate payoff and continuation value for American option holders. Without these penalties, the continuation value is equal to the actual funds obtainable by selling the option. When the sale proceeds achievable upon liquidation are lower due to penalties, immediate exercise becomes more advantageous, leading to a wider optimal early exercise region. We start studying the impact of liquidation penalties in discrete time, and provide closed-form solutions for perpetual American call options in the binomial model. In the continuous-time lognormal model, we derive closed-form asymptotic solutions near maturity for the critical price that triggers optimal early exercise. We also provide explicit pricing formulas for perpetual American options with liquidation penalties. Our results are relevant for executive stock options (ESOs), which typically exhibit liquidation penalties, and for the American equity options for which there is evidence of liquidation costs.