Options contracts come in two styles: American options, which allow holders to exercise the option rights at any time up until the day of expiration, and European options, which can be exercised only on the expiration date. Theoretically, an American call on a non-dividend-paying stock should never be exercised early because of the lost interest payments. Therefore, many researchers have concluded that the significant proportion of American options that are exercised early represent irrational decision making by investors.

However, this theory does not wholly account for intraday trading frictions. Options typically exhibit wide bid–ask spreads. In contrast to previous empirical studies based on closing prices and quotes, the authors consider intraday data. They define an exercise boundary violation (EBV) as a situation when the best bid price available for an option is lower than the option’s intrinsic value—that is, the amount by which it is currently in the money (ITM). They examine a large cross section of US equity options to discover how prevalent EBVs are—to find whether the theoretical argument against early exercise is applicable in practice.

The authors look at calls and puts on 2,945 stocks across all expiration months for 21 trading days during March 2010. To compare the prices for the options and the underlying stocks simultaneously, they use intraday price and quote data observed at one-minute intervals. They classify the ratios of strike price to stock price into three groupings representing the extent to which the options are ITM: deep ITM, mid ITM, and near ITM. They also set up three maturity categories: near term (one month to expiration or less), medium term (two to four months), and long term (over more months).

Using this sample, the authors determine the frequency with which EBVs arise in each of these categories, the EBVs’ magnitude, and their persistence (i.e., the extent to which they last throughout the trading day). The authors calculate the frequency and size of trades above and below the EBV boundary price to investigate whether options traders over the sample period avoided the most extreme boundary violations. They then examine the extent to which EBVs affect trading decisions, using logit regressions to compute the probability of options being exercised early.

The authors’ most important finding is “how common, persistent, and economically significant [exercise] boundary violations are.” Across the entire sample, 48.6% of options quotes exhibit EBVs. The best available bid across eight options exchanges is, on average, $0.31 below intrinsic value. The frequency of EBVs is particularly high among deep- and mid-ITM options with shorter maturity periods, whereas 90% or more of bids are below intrinsic value—in other words, in situations when the time value is low.

The authors also find that when investors elect to sell at EBV prices, the violations tend to be smaller than average—suggesting that the investors are reasonably successful in avoiding the worst boundary violations. Among all ITM options trades in the sample, just 12.77% of trading volume and 2.25% of trades occur below the boundary price—though this still represents a dollar loss of up to $32.9 million for the month from suboptimal trades.

Through their logit regressions estimating the likelihood of early exercise, the authors find (as expected) a strong relationship to “moneyness”—the probability that the option will still be ITM at maturity. They show that early exercise is significantly influenced by the existence of EBVs and their duration (the number of minutes during the trading day that an option exhibits a boundary violation).

The authors’ empirical findings dispute the theoretical principle that American call options should never be exercised early. In practice, the authors find that investors who exercise early may often be acting rationally because of the high incidence of EBVs. Such EBVs should not occur in a frictionless market, but their frequency and persistence demonstrate that liquidity issues are highly significant in options markets.

In theory, American options are worth the same as European ones with the same terms, which implies that the usual pricing model is equally good for both. But if, as the authors argue, early exercise of an American call can often be the optimal strategy for investors, then the pricing of American options relative to the equivalent European contracts needs to be reconsidered. A number of other issues also need to be reassessed, such as how investors should measure the effective bid–ask spread in the options market and how ITM options positions should be marked to market.

Furthermore, boundary violations have potential implications for the calculation of an option’s implied volatility. Typically, the implied volatility is determined from the bid–ask midpoint. However, under an EBV, the midmarket estimate will be biased—or even undefined, when the quote midpoint falls below intrinsic value.