American vs. European Options: Exercise, Dividends, and Pricing

Editorial responsibility: Oliver Sinz · Last verified: October 26, 2026

An American-style option can be exercised on any business day up to and including its last trading day. A European-style option can be exercised only at expiration. Both can be bought and sold in the market until trading in them ends: the exercise style limits when the holder can exercise, not when the position can be closed (OIC).

Most comparisons of American vs. European options stop there and add that American options cost more because they are more flexible. That is true in a narrow sense, since an American option is never worth less than an otherwise identical European one. But the extra right is often worth very little, and when it is worth something, the reasons are specific and measurable: interest on the strike price for in-the-money puts, upcoming dividends for in-the-money calls, and the assignment risk this creates for option writers. This guide quantifies each one, shows why the Black–Scholes–Merton formula values European options but not American puts, and compares the theory with how holders actually exercise.

All prices in this article are hypothetical model values, not market quotes. Nothing here is a recommendation to trade.

Exercise style is a contract term, not a location

The names do not indicate where an option trades. They date to Paul Samuelson’s 1965 paper on warrant pricing, which first used them for the two exercise conventions (Jarrow and Protter, 2004). Both styles trade around the world:

• In the U.S., standard listed options on individual stocks and ETFs are American-style. Most, but not all, index options are European-style (OIC).
• Cboe lists both styles on the same index: S&P 100 options trade as American-style OEX and European-style XEO (Cboe). SPX options on the S&P 500 are European-style (Cboe).
• In Japan, single-stock options on Osaka Exchange are European-style and can be exercised only on their last trading day (JPX). At Eurex, single-stock options are American-style except for a few designated contract groups, which are European-style (Eurex contract specifications, Eni options example).

Exercise style is also separate from settlement. OEX options are American-style and settle in cash; Eurex’s European-style stock options settle by delivery of shares. OCC describes European-style options as exercisable only “during a specified period before expiration,” typically the expiration date itself (OCC).

Several differences that traders associate with exercise style actually come from the product. Standard AM-settled SPX options stop trading on the business day before their settlement value is calculated, while PM-settled SPXW options trade on expiration day (Cboe). The reliable way to know a contract’s exercise style, settlement method, and last trading day is its specifications.

How the two styles compare in value

Two results from Merton (1973) frame everything that follows:

1. An American option is worth at least as much as an otherwise identical European option. It carries every right of the European option plus one more.
2. An American call on a stock that pays no dividend during the option’s life should never be exercised early, provided the risk-free rate is not negative. It is then worth exactly as much as the European call.

The second result rests on a lower bound. Before expiration, a call on a non-dividend-paying stock is worth at least the stock price minus the present value of the strike, S − PV(K). With a positive rate, that is more than the S − K that exercise delivers. Exercising pays the strike early and discards the call’s protection against a fall below the strike. Suppose a stock trades at $120 and a 100-strike call has 30 days left, with a 4% rate and 25% volatility. Exercise yields $20.00. The lower bound alone is $20.33, and the model value is $20.34. A holder who no longer wants the position does better selling the call than exercising it, before frictions. OIC makes the same point: exercising forfeits whatever time value the option still has (OIC). The argument fails if rates are negative: PV(K) then exceeds K, paying the strike early saves money instead of forgoing interest, and early exercise of a deep in-the-money call can be optimal even without dividends.

An American option is also never worth less than its intrinsic value, because it can be exercised immediately. A European option can be, and when interest rates are positive, deep in-the-money European puts often are. That is not an arbitrage for the owner, who cannot exercise until expiration.

In standard models with nonnegative rates, then, the early-exercise premium (the American value minus the European value) has two sources: interest earned by receiving the strike early, which matters for puts, and dividends collected by owning the stock before it goes ex-dividend, which matter for calls.

American puts: interest on the strike vs. remaining protection

Hypothetical assumptions for this section:

• Stock XYZ, no dividends; 100-strike put with six months (0.5 year) to expiration
• 25% volatility and a 4.0% continuously compounded risk-free rate, both constant
• European values from Black–Scholes–Merton (Black and Scholes, 1973); American values from a binomial tree (average of 6,000 and 6,001 steps), cross-checked against a finite-difference solver
• Critical exercise prices from a fine-grid finite-difference solver, rounded to the nearest $0.10
• Values per share; a standard U.S. equity option contract covers 100 shares

Premiums are calculated from unrounded values, so a few differ by a cent from the rounded columns.

At the money, the right to exercise early adds about $0.18 per share, roughly $18 per contract or 2.8% of the American put’s value. Deep in the money it is worth much more: at $70 the American put is worth its full $30 intrinsic value, while the European put is worth $28.18.

Why exercise a put early. For European options, put-call parity gives P = PV(K) − S + C, where C is the same-strike call. At $70, the present value of the $100 strike is $98.02, and the call is worth $0.16, so the European put is worth $98.02 − $70 + $0.16 = $28.18. Exercising now pays $30.00. The difference reflects the trade-off: exercising collects the strike six months early, worth $1.98 of interest, and gives up the protection the call represents, worth $0.16. When the interest dominates, immediate exercise wins.

The critical price. For each time to expiration there is a stock price, S*, at or below which exercising immediately is optimal in the model:

The boundary rises toward the strike as expiration approaches, because less time value remains to be given up.

Below intrinsic value does not mean “exercise now.” With six months left, the European put falls below intrinsic value once XYZ drops under about $85.28. Between about $77.50 and $85.28, the European put is worth less than immediate exercise, yet the American holder should still wait. At $80, the American put is worth $20.07, more than its $20.00 intrinsic value, because the right to exercise later is worth more than exercising today.

Interest rates drive the premium. The same six-month put at different rates:

At a zero interest rate and with no dividends, early exercise of a put never pays and the two styles are worth the same. The premium grows with the rate because receiving the strike early is worth more. Kim (1990) showed that the premium can be written exactly in these terms: it is the present value of the interest earned on the strike in the states where the holder would exercise.

Dividends push in the opposite direction for puts. A put holder expects the stock to fall by roughly the dividend on the ex-dividend date, so exercising just before that date gives up the drop. Expected dividends therefore delay early exercise of puts and shrink their early-exercise premium.

American calls and dividends: the last cum-dividend day

A call holder does not receive dividends, and ordinary cash dividends do not trigger an adjustment to listed option terms. OCC generally adjusts only for non-ordinary cash dividends of $0.125 per share or more (SEC Release 34-99641). To collect a dividend, a call holder must exercise and own the shares. OIC explains that a holder who exercises before the ex-dividend date is entitled to the dividend, and that an assigned writer must then deliver the shares plus the dividend (OIC). Under the T+1 settlement cycle, the ex-dividend date for a regular dividend is normally the same business day as the record date (SEC filing, NYSE Arca). In practice, the holder must submit exercise instructions on the business day before the ex-date, the last cum-dividend day, within the brokerage firm’s exercise cut-off.

In standard models with discrete dividends and a nonnegative interest rate, early exercise of a call can be optimal only just before an ex-dividend date (Roll, 1977; Geske, 1979; Whaley, 1981). At that moment the holder compares two choices:

• Exercise: pay K for a stock worth S, a value of S − K.
• Hold: keep a call on a stock that is about to fall by the dividend D.

If no further dividends are expected before expiration, put-call parity for the remaining life turns this comparison into a simple rule. Exercise just before the ex-date only if:

D > P + K × (1 − e^(−rτ))

Here P is the value, just after the ex-date, of a European-style put with the same strike and expiration (a listed American put would be worth slightly more), r is the risk-free rate, and τ is the time from the ex-date to expiration. In words, the dividend must exceed both the interest lost by paying the strike early and the downside protection given up, which is exactly what the put is worth. If the dividend is smaller than the interest on the strike alone, early exercise is never optimal, however deep in the money the call is.

Hypothetical example. XYZ trades at $100 and will go ex-dividend on a $1.00 dividend in 30 days. The options expire 30 days after that, 60 days from today. Volatility is 25% and the rate is 4%. The stock follows the “escrowed dividend” convention: the price minus the present value of the known dividend follows the model’s lognormal process, and the stock falls by exactly $1.00 on the ex-date. American values come from the Roll–Geske–Whaley formula and agree with a 6,000-step binomial tree to within $0.0001.

The decision for the 90 call on the last cum-dividend day, with 30 days left after the ex-date:

The gain from exercising equals the dividend minus the interest minus the put. At $100 it is $1.00 − $0.30 − $0.26 = $0.44 per share, or $44 per contract. It can never exceed about $0.70 here, the $1.00 dividend minus $0.30 of interest, no matter how deep in the money the call is. For the 100 strike, the interest over the same 30 days is $0.33, so a $0.30 dividend would never justify early exercise.

Real decisions also depend on bid-ask spreads, the cost of carrying the stock, taxes, and the actual price on the last cum-dividend day. And for a writer, whether a particular short call is assigned depends on what other holders do, as discussed below.

American option pricing: why Black–Scholes is not enough

The Black–Scholes–Merton formula values a European option. It also gives the right value for an American call on a non-dividend-paying stock, because that call is never exercised early as long as the interest rate is not negative. What it cannot value is the early-exercise right of an American put, or of a call before a dividend. There, the holder’s optimal exercise boundary is part of the solution, a “free-boundary” problem with no general closed-form answer. Practitioners use numerical methods instead. For the at-the-money put above (XYZ and strike at $100, six months, 25% volatility, 4% rate):

• Binomial trees (Cox, Ross, and Rubinstein, 1979) check at every node whether exercising beats continuing. They converge, but oscillate between odd and even step counts, so averaging adjacent step counts helps.
• Finite-difference methods (Brennan and Schwartz, 1977) solve the pricing equation on a price-and-time grid, with the exercise value as a floor at every point.
• Analytic approximations such as Barone-Adesi and Whaley (1987) are fast but less precise. Here the error grows from about $0.01 at the money to about $0.07 with XYZ at $85.
• Simulation with regression (Longstaff and Schwartz, 2001) handles path-dependent payoffs and multiple risk factors. With a finite set of exercise dates, it technically values a Bermudan option, one exercisable only on specified dates, which is worth slightly less than the American option. Its results also carry sampling error; the gap in the table is within one standard error.
• Calls with one known dividend have an exact formula under the escrowed-dividend model, the Roll–Geske–Whaley formula used in the dividend example.

Implied volatility. Feeding American put prices into the European formula overstates implied volatility, because the formula attributes the early-exercise premium to volatility. With true volatility of 25%:

The distortion is largest for in-the-money puts and could be mistaken for a volatility skew. Implied volatility for American-style contracts should come from a model that prices early exercise, using the same rate and dividend assumptions as the rest of the analysis.

Parity becomes a range. For European options on a non-dividend-paying stock, put-call parity is an equality: C − P = S − PV(K). For American options it holds only as a pair of bounds, because one of the two options may be exercised early. With a nonnegative rate, that option is the put, and S − K ≤ C − P ≤ S − PV(K). With a negative rate, it is the call, and the bounds swap: S − PV(K) ≤ C − P ≤ S − K.

Theory vs. practice: how exercise actually happens

The models assume that holders exercise exactly when it is optimal and trade without costs. Real behavior departs from both assumptions.

• Most options are never exercised. OIC reports that, historically, more than 72% of option contracts are closed out in the market before expiration, about 22% expire worthless, and about 6% are exercised (OIC).
• Holders often fail to exercise when the model says they should. Studying U.S. stock puts from January 1996 to September 2008, Barraclough and Whaley (2012) found more than 3.96 million puts, over 3.7% of puts outstanding, that should have been exercised early but were not. The failure cost holders about $1.9 billion in forgone interest, much of it captured by market makers and proprietary trading firms. Around ex-dividend dates, Hao, Kalay, and Mayhew (2010) found that a significant fraction of the call open interest that a rational exercise policy would have exercised remained unexercised, a windfall for writers who were not assigned. Short-term traders captured part of that windfall with heavy trading on the last cum-dividend day. Pool, Stoll, and Whaley (2008) document the same failure to exercise calls.
• Holders sometimes exercise early for reasons the frictionless model leaves out. Jensen and Pedersen (2016) show that frictions can make early exercise the better choice, for example when exercising avoids the cost of shorting the stock, a wide option spread, or financing charges. They document billions of dollars of early exercise. Their model explains up to 98% of early exercises by market makers and 67% by customers. The simplest case: when an in-the-money option’s bid is below its intrinsic value, exercising captures more than selling.
• Market quotes do not always follow the model’s ordering. Comparing OEX and XEO options on the same index, Li, Zhang, Ruan, and Aschakulporn (2024) found that the European XEO mid-quote can exceed the mid-quote of an otherwise identical American OEX option, a gap they attribute to liquidity.

For writers, assignment is probabilistic. OCC assigns exercise notices randomly among its clearing members, which then assign them to customer accounts under their own procedures (OIC). A writer of an American-style option can be assigned on any day the option is exercisable (OCC), whether or not exercise was optimal for the holder, and can escape assignment on a day when it was. A writer of a European-style option cannot be assigned before expiration. That writer still bears the price risk until settlement and, for options settled on an opening value, the gap between the last trade and the settlement value. On expiration day itself, holders of expiring equity options have until 5:30 p.m. ET to make final exercise decisions, and brokerage firms may set earlier deadlines (FINRA).

American vs. European options side by side

Neither style is better in general. In fair pricing, the holder pays for the early-exercise right and the writer is compensated for granting it; how much it is worth depends on moneyness, rates, dividends, and time. Comparisons between different products, such as SPX options and options on an S&P 500 ETF, involve more than exercise style: contract size, settlement method, settlement timing, and dividends also differ, so exercise style explains only part of any price difference between them.

Key takeaways

• Exercise style determines when the holder can exercise, not where the option trades or whether it can be sold before expiration. Exercise style, settlement method, and last trading day are separate contract terms.
• An American option is worth at least as much as an otherwise identical European option and never less than its intrinsic value. An American call on a stock that pays no dividends is worth the same as the European call, as long as interest rates are not negative.
• Early exercise of a put pays when the interest earned on the strike outweighs the protection given up. The premium rises with interest rates and disappears at a zero rate without dividends. A European put trading below intrinsic value does not by itself mean an American holder should exercise.
• In the frictionless model with a nonnegative rate, early exercise of a call can pay only just before an ex-dividend date. With no further dividends before expiration, it pays only if the dividend exceeds the value of the same-strike European put after the ex-date plus the interest on the strike.
• Black–Scholes–Merton values European options and, when rates are not negative, American calls on non-dividend-paying stocks. American puts, and calls facing dividends, require numerical or approximate methods, and inverting the European formula on their prices overstates implied volatility.
• Real exercise decisions depart from the model in both directions, so writers of American-style options face assignment risk that no formula pins down.

Primary sources

• Options Industry Council: Options Exercise FAQ · What is the difference between American-style and European-style options?
• Options Clearing Corporation: Characteristics and Risks of Standardized Options · Key Information Document, Standardized Equity Option (Short Put)
• SEC: Release 34-99641, OCC interpretive guidance on cash dividend adjustments · Release 34-99881, NYSE Arca ex-dividend dates under T+1
• FINRA: Exercise Cut-Off Time for Expiring Options
• Cboe: S&P 100 Index Options (OEX and XEO) · SPX Options Product Specifications
• Japan Exchange Group: Securities Options Contract Specifications · Eurex: Equity Options Contract Specifications (Eni options example)
• Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, 4(1), 141–183.
• Black, F., and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637–654.
• Roll, R. (1977). An Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends. Journal of Financial Economics, 5(2), 251–258.
• Geske, R. (1979). A Note on an Analytical Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends. Journal of Financial Economics, 7(4), 375–380.
• Whaley, R. E. (1981). On the Valuation of American Call Options on Stocks with Known Dividends. Journal of Financial Economics, 9(2), 207–211.
• Brennan, M. J., and Schwartz, E. S. (1977). The Valuation of American Put Options. Journal of Finance, 32(2), 449–462.
• Cox, J. C., Ross, S. A., and Rubinstein, M. (1979). Option Pricing: A Simplified Approach. Journal of Financial Economics, 7(3), 229–263.
• Barone-Adesi, G., and Whaley, R. E. (1987). Efficient Analytic Approximation of American Option Values. Journal of Finance, 42(2), 301–320.
• Kim, I. J. (1990). The Analytic Valuation of American Options. Review of Financial Studies, 3(4), 547–572.
• Longstaff, F. A., and Schwartz, E. S. (2001). Valuing American Options by Simulation: A Simple Least-Squares Approach. Review of Financial Studies, 14(1), 113–147.
• Jarrow, R., and Protter, P. (2004). A Short History of Stochastic Integration and Mathematical Finance: The Early Years, 1880–1970. IMS Lecture Notes – Monograph Series, 45, 75–91.
• Pool, V. K., Stoll, H. R., and Whaley, R. E. (2008). Failure to Exercise Call Options: An Anomaly and a Trading Game. Journal of Financial Markets, 11(1), 1–35.
• Hao, J., Kalay, A., and Mayhew, S. (2010). Ex-dividend Arbitrage in Option Markets. Review of Financial Studies, 23(1), 271–303.
• Barraclough, K., and Whaley, R. E. (2012). Early Exercise of Put Options on Stocks. Journal of Finance, 67(4), 1423–1456.
• Jensen, M. V., and Pedersen, L. H. (2016). Early Option Exercise: Never Say Never. Journal of Financial Economics, 121(2), 278–299.
• Li, W., Zhang, J. E., Ruan, X., and Aschakulporn, P. (2024). An Empirical Study on the Early Exercise Premium of American Options: Evidence from OEX and XEO Options. Journal of Futures Markets, 44(7), 1117–1153.