American options with liquidation penalties

De Donno Marzia, Università Cattolica di Milano

In an arbitrage-free complete market we study American options with liquidation penalties. Liquidation penalties are frequent in executive stock options (ESOs), where liquidation can be completely forbidden or mildly deterred via liquidation penalties. In ESOs liquidation penalties aim at lowering the chances of selling the ESOs and the underlying company shares. Together with vesting periods, that allow the option to be exercised only after a given period of time or if a prespecified performance measure reaches the desired level, liquidation penalties aim at providing executives with the incentives to increase the company shares value. We show that liquidation penalties in American options lower the continuation value for the holder of the option. Consequently, even mild liquidation penalties trigger the existence of optimal exercise opportunities for the American options with liquidation constraints that are absent when the option can be fully liquidated. Thus, liquidation penalty make the holder exercise for lower share values than the frictionless critical price, which goes in the opposite direction of the desired incentive.

Area: CS20 - Stochastic Modeling in Finance and Insurance I (Tiziano de Angelis)

Keywords: Liquidation penalties; Executive stock options; Optimal stopping; American options; Early Exercise

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