Options: calls, puts, strike and expiry

In plain language — An option buyer pays a premium to obtain a right. The seller receives the premium and assumes the corresponding obligation if the contract is exercised or assigned.

An option is a derivative contract whose value depends on an underlying. The buyer, also called the holder, obtains a right; the seller, or writer, assumes the opposite obligation.

a call gives the buyer the right to buy under the contract's terms;
a put gives the buyer the right to sell.

The definition does not imply that every option can be exercised at any time or that the underlying is always delivered. Style, settlement and specifications vary.

Contract elements

Element	Question
Underlying	which asset, index, future, rate or other reference?
Type	call or put?
Strike	at what price does the right apply?
Expiry	when does the contract end?
Premium	how much does the buyer pay and the seller receive?
Multiplier	how many economic units does one contract represent?
Exercise style	when can it be exercised?
Settlement	physical delivery or a cash difference?

“One contract represents 100 shares” is a common convention for many U.S. equity options, not a universal rule. Corporate actions and specifications can change the deliverable.

The contract defines rights and obligations; terminal payoff must be distinguished from the result after premium and from value before expiry.

Payoff and result at expiry

Let:

S_T be the underlying price at expiry;
K be the strike;
P be the premium per unit.

Before costs, interest, taxes and the multiplier:

call payoff = max(S_T − K, 0)
put payoff  = max(K − S_T, 0)

long-call result = call payoff − P
long-put result  = put payoff − P

The payoff is the terminal value of the right; the result subtracts the premium paid. For the seller of the same option, with the same premium and before other costs, the result is the opposite. These formulas do not describe the option's price before expiry.

Neutral example: a call with a strike of 100 and a premium of 4.

Underlying at expiry	Intrinsic value	Long-call result
90	0	−4
100	0	−4
104	4	0
115	15	+11

The example's break-even point at expiry is 104 before costs. It is neither a probability of success nor a guaranteed price.

Moneyness

The relationship between the underlying and the strike is described as:

in the money (ITM) — exercise would have positive intrinsic value;
at the money (ATM) — the underlying and strike are close under the convention used;
out of the money (OTM) — there is no current intrinsic value.

For a call, ITM means the underlying is above the strike; for a put, it means the underlying is below the strike. An OTM option may have market value because time and the possibility of a move remain.

What determines the premium

The price incorporates several dimensions:

the underlying level relative to the strike;
time remaining;
volatility expected by the market;
rates and cash flows of the underlying;
demand, supply and liquidity;
style, settlement and contract features.

The simplest educational decomposition distinguishes intrinsic value and time or extrinsic value. In practice, premium valuation is a joint problem: price, time, volatility, rates, cash flows and conventions interact. A tradable quote and a model-produced value are not necessarily equal.

Delta, gamma, theta and vega measure local sensitivities, not guaranteed profits. The four entries are connected in Risk allocation and sensitivities; rho, implied volatility, smile, skew and multi-leg strategies belong to Options and volatility.

Exercise, assignment and expiry

American style: exercise is allowed on multiple dates up to expiry, according to the contract;
European style: exercise takes place at expiry;
other contracts may have different windows or conditions.

When a buyer exercises, a seller may receive an assignment. The outcome may be delivery of the underlying, the opening of a futures position or cash settlement.

European style restricts when exercise is allowed; it does not prevent a holder from selling, or a writer from repurchasing, the contract before expiry when a market exists. Expiry date, last trading day, broker cutoff and any automatic-exercise process are not identical by definition. Read the relevant specifications and procedures; see Exercise, assignment and settlement.

Automatic exercise, thresholds, times and the ability to submit instructions depend on the clearing house, broker and contract. An apparently small position can create a much larger exposure after assignment.

Buyers and sellers face asymmetric risks

Buyer

For a fully paid long option, the contractual loss is generally limited to the premium and costs. “Limited” can still mean losing 100% of the capital allocated to the option, even rapidly.

Seller

The writer receives a premium but assumes an obligation:

a short put can produce a substantial loss if the underlying collapses;
an uncovered call can have a theoretically unlimited loss because the underlying has no ceiling;
margin and liquidation may intervene before expiry;
gaps and volatility can make the position difficult to close.

A covered position, a spread and an uncovered sale do not carry the same risk. The strategy's name is no substitute for the aggregate payoff of all its legs.

Economic uses

hedging an existing exposure;
directional exposure with a nonlinear payoff;
managing the distribution of outcomes;
transferring volatility risk;
constructing conditional payoffs.

A hedge has a cost and may be imperfect because of strike, expiry, basis, liquidity or quantity. Selling options to “generate income” does not turn the premium into a risk-free return.

Main risks

total loss of the premium;
leverage and multiplier;
time decay;
changes in implied volatility;
spread and liquidity by strike/expiry;
early exercise and assignment;
writer margin and liquidation;
gaps in the underlying;
model and correlation risk in strategies;
complexity across multiple legs;
differences among listed, OTC and binary options and structured products.

Common mistake — Treating the premium received as final profit. It is the consideration for an obligation that can generate a much larger loss.

Checklist

What is the exact underlying?
Call or put, bought or sold?
Strike, expiry, multiplier and deliverable?
Exercise style and settlement type?
Maximum payoff, maximum loss and intermediate scenarios for the whole position?
Effect of time and volatility, not direction alone?
Spread, volume, open interest and quote quality?
The broker's margin, assignment and expiry-instruction rules?

Sources

The Options Clearing Corporation, Characteristics and Risks of Standardized Options — official U.S. disclosure on contract features, exercise, assignment, settlement and combination risks.
U.S. Securities and Exchange Commission, Investor.gov, An Introduction to Options, published 18 March 2015 and updated 16 July 2026.
U.S. Securities and Exchange Commission, Investor.gov, Opening an Options Trading Account, updated 16 July 2026 — risks, approval and disclosure in the U.S. regulatory context.
U.S. Commodity Futures Trading Commission, Futures Market Basics — options on futures and contractual obligations.
European Securities and Markets Authority, MiFID II, Annex I — Lists of services and activities and financial instruments — categories of options and other derivatives in the EU framework.