On Valuing American Futures Options

Abstract

More than 20 different futures option contracts currently trade on U.S. exchanges. These options are exercisable at any time up to including the expiration day. In pricing them, however, investment managers have been forced to rely on principles developed for 'European options, which may be exercised only at expiration. This practice can be misleading, because the early exercise privilege of American futures options has a significant effect on pricing. The early exercise premium of American futures options affects two types of pricing relations. The first type are those relations developed by assuming the market is free from costless arbitrage opportunities. These relations are often termed rational option pricing restrictions, and an important relation within this category is the put-call parity relation, which simultaneously links the prices of the put the call in the futures option market with the price of the underlying futures contract. The second perhaps most important type of option pricing relations affected by early exercise are valuation equations. Valuation equations require an additional assumption about the futures price distribution; the most commonly used assumption is a lognormal distribution. The widest known model for pricing futures option contracts is the Black model, but it was developed for European futures options thereby ignores the value of the early exercise feature of the American options. An intuitively appealing approximation method based on the American futures option valuation equation is very accurate computationally inexpensive.