Long Call
Payoff = max(ST − K, 0)
Right to buy at K. Profit unlimited above breakeven (K + premium). Max loss = premium paid.
Long Put
Payoff = max(K − ST, 0)
Right to sell at K. Profit rises as S falls below breakeven (K − premium). Max loss = premium paid.
Short Call
Payoff = −max(ST − K, 0)
Obligation to sell at K if exercised. Max gain = premium. Loss unlimited above K + premium.
Short Put
Payoff = −max(K − ST, 0)
Obligation to buy at K if exercised. Max gain = premium. Max loss = K − premium.