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Optionsbeginner

American vs European Options

American options can be exercised at any business day up to and including expiry. European options can be exercised only at expiry. Because the American holder has every European holder's choices plus more, CAm≥CEuC_{\text{Am}} \geq C_{\text{Eu}} and PAm≥PEuP_{\text{Am}} \geq P_{\text{Eu}}. The naming refers to exercise style, not where the option is listed. On the ASX, equity options are American-style while S&P/ASX 200 (XJO) index options are European-style and cash-settled.

Why it matters

American options carry an early-exercise option on top of the European right at expiry. Optionality is always worth at least zero, so American options dominate. The size of the gap depends on whether early exercise is ever optimal. For a call on a non-dividend stock, Merton (1973) showed it is never optimal to exercise early, so the American and European prices coincide. For an American put that is deep in the money, the holder can lock in K−SK - S now and earn interest on the proceeds, which makes early exercise potentially optimal and creates a real early-exercise premium.

Formulas

Value inequality
CAm≥CEuandPAm≥PEuC_{\text{Am}} \geq C_{\text{Eu}} \quad \text{and} \quad P_{\text{Am}} \geq P_{\text{Eu}}
Strict inequality holds whenever early exercise is potentially optimal, otherwise the two prices are equal.
Early-exercise premium
EEP=VAm−VEu≥0\text{EEP} = V_{\text{Am}} - V_{\text{Eu}} \geq 0
The extra dollar value of the American flexibility. Typically small for calls on non-dividend stocks, larger for deep ITM puts.

Worked examples

Scenario

An American put on a non-dividend stock is deep in the money with S=S = 10,, K = $50$, and 6 months to expiry.

Solution

Exercising now locks in K−S=K - S = 40$ which can be invested at the risk-free rate. A European put holder must wait until expiry and forgoes that interest. The American holder may therefore exercise early, and the early-exercise premium can be a meaningful fraction of the option price for short-rate environments above zero.

Scenario

An American call on a non-dividend stock has S=S = 60,, K = $50$, and 3 months to expiry.

Solution

By Merton (1973), early exercise is never optimal. Selling the option realises both intrinsic value and remaining time value, while exercising forfeits the time value. The American and European calls have identical prices here. Black-Scholes-Merton can therefore be used for both.

Common mistakes

  • ✗American and European refer to where the option trades. They refer only to exercise timing. ASX-listed XJO index options are European-style, while ASX equity options on companies like BHP and CBA are American-style.
  • ✗American options are always strictly more valuable than European ones. They are equal in value for calls on non-dividend stocks, by Merton (1973). The strict premium only appears when early exercise can be optimal, such as for puts or for calls on dividend payers near ex-dividend dates.
  • ✗All US-listed options are American. Index options like S&P 500 SPX are European-style and cash-settled, while SPY ETF options are American-style. The exercise style is a contract specification, not a regional convention.

Revision bullets

  • •American: exercise anytime up to TT
  • •European: exercise only at TT
  • •Always VAm≥VEuV_{\text{Am}} \geq V_{\text{Eu}}
  • •ASX equity options are American. XJO index options are European
  • •Early exercise of call on no-dividend stock is never optimal (Merton 1973)

Quick check

Why is an American option worth at least as much as an otherwise identical European option?

Which ASX product is European-style?

Connected topics

1-Step TreeEarly ExerciseBSM Intro

In learning paths

Options Path

Sources

  1. Hull (2022), §11.5, §11.6
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Develops the inequality $V_{\text{Am}} \geq V_{\text{Eu}}$ and shows when early exercise is and is not optimal.
  2. Merton (1973), §4
    Merton, Robert C. "Theory of Rational Option Pricing." Bell Journal of Economics and Management Science, vol. 4, no. 1, 1973, pp. 141 to 183.
    Proves that early exercise of an American call on a non-dividend stock is never optimal, so $C_{\text{Am}} = C_{\text{Eu}}$ in that case.
  3. ASX Module 9: Index Options
    Australian Securities Exchange. Online Options Course, Module 9: Index Options. ASX Investor Education, accessed 2026.
    Confirms that XJO and other ASX index options are European-style and cash-settled, in contrast to American-style equity options.
  4. ASX Options Contract Specifications
    Australian Securities Exchange. Options Contract Specifications. ASX Investor Education, accessed 2026.
    Official specifications for ASX equity options including American exercise style and expiry on the Thursday before the last business Friday of the month.
How to cite this page
Dr. Phil's Quant Lab. (2026). American vs European Options. Derivatives Atlas. https://phucnguyenvan.com/concept/american-vs-european
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