An American Call IS Worth More Than a European Call: The Value of American Exercise When the Market Is Not Perfectly Liquid

Abstract

An easily proved theoretical principle in option pricing is that an American call option should never be exercised early, except possibly just before an ex-dividend date. This result depends on the ability to liquidate an option position, European or American, for its theoretical value (the European call price) in the market. But this is normally impossible in a real world option market, where the best bid for an in-the-money short maturity option is generally below intrinsic value even for an option on a liquid stock. An American option can always be exercised to recover intrinsic value while a European contract must be liquidated at the best available bid in the market. If an investor has to exit an American call position before maturity, exercise can often return more than selling at the market's best bid. This paper derives the value of liquidity-based early exercise of both calls and puts in closed-form, as a function of the bid-ask spread. An illustrative example using a small amount of market data shows that the value of Americanness can be substantial, even for the most actively traded options whose spreads are very tight. For somewhat less active options the premium for liquidity-based early exercise can easily exceed the theoretical value of the early exercise option for an American put or a call on a typical dividend-paying stock.