Call vs Put Options: Rights, Obligations and Payoff at Expiration

A call option gives its buyer the right, but not the obligation, to buy 100 shares of the underlying at a fixed price (the strike) until expiration. A put option gives its buyer the right to sell 100 shares at the strike. The buyer pays a price, the premium, for that right; the seller receives the premium and takes on the obligation to deliver or take the shares if the option is exercised.

Call Vs Put: Rights And Obligations

	Call	Put
Buyer (holder, "long")	Right to buy shares at the strike	Right to sell shares at the strike
Seller (writer, "short")	Obligation to sell shares at the strike if assigned	Obligation to buy shares at the strike if assigned
Buyer pays	Premium	Premium
Seller receives	Premium	Premium

The buyer decides whether to exercise. The seller has no choice: if assigned, the seller must complete the trade. For standard US equity and ETF options, one contract covers 100 shares, and quoted premiums are per share.

Call Option Payoff At Expiration

With S the share price at expiration and K the strike:

Call value at expiration = max(S − K, 0)
Call buyer's profit = max(S − K, 0) − premium
Call seller's profit = premium − max(S − K, 0)
Breakeven = K + premium

The call buyer's largest possible loss is the premium. The call seller's largest possible loss has no fixed limit, because the share price has no upper limit.

Put Option Payoff At Expiration

Put value at expiration = max(K − S, 0)
Put buyer's profit = max(K − S, 0) − premium
Put seller's profit = premium − max(K − S, 0)
Breakeven = K − premium

The put buyer's largest possible loss is the premium. The put seller's largest possible loss is K − premium per share, reached if the share price falls to zero.

Illustrative example: a call and a put on the same stock, both with a strike of $50, cost $2.00 and $1.50 per share. At expiration:

Share price	Call value	Call buyer's profit	Put value	Put buyer's profit
$40	$0	−$2.00	$10.00	+$8.50
$50	$0	−$2.00	$0	−$1.50
$55	$5.00	+$3.00	$0	−$1.50
$60	$10.00	+$8.00	$0	−$1.50

Per contract, multiply by 100. In each row the seller's profit is the buyer's profit with the sign reversed, before commissions.

What Is An Option Premium?

The premium is the market price of the option. It has two parts: intrinsic value, what the option would be worth if exercised now, and extrinsic (time) value, the rest. See intrinsic vs extrinsic value. The premium depends on the share price, the strike, the time to expiration, interest rates, expected dividends and implied volatility.

Calls And Puts Before Expiration

The formulas above describe value at expiration. Before then an option's price also contains time value, so it is usually worth more than max(S − K, 0) or max(K − S, 0). How the price responds to the share price, time and volatility is described by the option Greeks.

What Calls And Puts Do Not Tell You

Open calls or puts do not reveal whether their holders are buyers or sellers, hedging or speculating. Volume and open interest count contracts, not intent.
A large amount of call or put activity is not, by itself, a measure of direction. See put/call ratio.

Sources

The Options Clearing Corporation (OCC), Characteristics and Risks of Standardized Options, the options disclosure document: the rights and obligations of option holders and writers, and standard contract terms.
John C. Hull, Options, Futures, and Other Derivatives (Pearson, many editions): payoffs at expiration, premium, and the inputs to option prices.
Fischer Black and Myron Scholes, "The Pricing of Options and Corporate Liabilities", Journal of Political Economy (1973): option pricing before expiration.