Exercise Styles: American vs European

Options come in two exercise styles that determine when you can exercise them.

Quick Comparison

	European	American
Exercise timing	Only at expiry	Any time before expiry
Pricing	Simpler (Black-Scholes)	More complex (binomial)
Premium	Lower	Higher (flexibility premium)
Early exercise risk	None	Seller faces early assignment
Common for	Index options, crypto	Stock options

European Style

European options can only be exercised at expiration. You hold the contract until expiry, then it settles based on the final price.

Why this matters:

• Simpler pricing models work (Black-Scholes assumes European exercise)
• No early assignment risk for sellers
• You know exactly when settlement happens

Hypercall uses European style

All options on Hypercall are European. You don't need to worry about early exercise - positions settle automatically at 08:00 UTC on expiry day.

American Style

American options can be exercised any time before expiration. The holder can choose to exercise early if it's profitable.

Why someone might exercise early:

• Capture a dividend (for stock options)
• Lock in deep ITM profit
• Avoid time decay on a winning position

The catch: This flexibility costs more. American options trade at a premium over equivalent European options.

Short answer: Only when there's a reason to exercise early.

If we assume no dividends and no interest rates, American and European options are priced identically. There's simply no benefit to exercising early - you'd just give up the remaining time value.

Why dividends matter (for calls): When a stock pays a dividend, the stock price drops by the dividend amount on the ex-date. If you hold a deep ITM call, you might want to exercise before the ex-date to capture that dividend. This early exercise flexibility has value, so American calls cost more than European calls when dividends are expected.

Why interest rates matter (for puts): If you exercise a put early, you receive cash (the strike price) immediately. With positive interest rates, you can invest that cash and earn interest. This makes early exercise attractive for deep ITM puts, so American puts cost more than European puts when rates are high.

Try it yourself: Use the sliders below to see how dividend yield and interest rates create a pricing difference between American and European options.

Stock (for dividend yield)

Dividend Yield5.0%

Higher = more early exercise value

Interest Rate0.0%

Lower = more early exercise value

ATM Option Prices

European$7.17

American$7.26

Difference+$0.09 (1.3%)

Early Exercise Premium (American − European)

American costs more! With a 5.0% dividend yield, call holders might want to exercise early to capture the dividend. This flexibility has value.

Why Crypto Uses European

Most crypto options platforms (including Hypercall) use European style because:

1. No dividends - The main reason to exercise American options early doesn't apply
2. Simpler margining - No early assignment means predictable collateral requirements
3. Better pricing - Cleaner math, tighter spreads
4. 24/7 markets - Settlement timing is well-defined (08:00 UTC)

For tokenized real-world assets that pay dividends (like tokenized stocks), the expected dividend is typically priced into the option via the funding rate on the perpetual. Longs effectively receive dividends through funding payments, so the option price already reflects anticipated payouts, removing the early exercise incentive that exists in traditional markets.

For the math: Non-Arbitrage Conditions for Perpetual Forwards

Formula Note

For European options, the payoff at expiry is:

• Call: max(S − K, 0)
• Put: max(K − S, 0)

Where S is the settlement price and K is the strike.

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Exotics

Beyond vanilla calls and puts, there are exotic options with non-standard payoff structures:

• Binary/Digital - Fixed payout if ITM, zero if OTM
• Barrier - Activates or deactivates at a price threshold
• Asian - Payoff based on average price over time
• Lookback - Payoff based on max/min price during life

Hypercall focuses on vanilla European options, but understanding exotics helps contextualize the broader derivatives landscape.

Binary Options = Prediction Markets

Platforms like Polymarket and Kalshi are essentially binary options markets:

Prediction Market	Binary Option Equivalent
"Will BTC be above $100k on Dec 31?"	Binary call, strike $100k, expiry Dec 31
"Will ETH be below $2k?"	Binary put, strike $2k
Pays $1 if YES	Fixed payout if ITM
Pays $0 if NO	Expires worthless if OTM

The share price (e.g., $0.65) represents the market's implied probability, just like a binary option's price reflects ITM probability.

Binary vs Vanilla Payoffs

Binary Option

Fixed payout: all-or-nothing at strike

Vanilla Call

Linear payout: unlimited upside above strike

Binary call (strike K, payout P):

• If S > K at expiry: receive P
• If S ≤ K at expiry: receive 0

Vanilla call (strike K):

• If S > K at expiry: receive (S − K)
• If S ≤ K at expiry: receive 0

The key difference: vanilla options have unlimited upside. Binary options have a capped payout regardless of how far ITM.

Why vanilla wins for most use cases: Binary options have delta that spikes near the strike at expiry, making them hard to hedge. Vanilla options have smoother greeks and are better for expressing leveraged directional views with unlimited upside.

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Related:

• Cash vs Physical Settlement
• Lesson 1: What is an Option? - Full explainer with examples