Arbitrage is the act of buying and selling the same asset, or two assets with equivalent payoffs, in a way that locks in profit from a price difference.
The core idea
If the same payoff can be purchased more cheaply in one place than another, a trader can buy low and sell high. In the simplest case, an arbitrage opportunity exists when:
$$ P_A < P_B - c $$
where (P_A) is the lower price, (P_B) the higher price, and (c) the total cost of executing the trade.
Why arbitrage matters
Arbitrage is one of the main forces pushing markets toward the law of one price. When enough traders exploit a gap, the cheap asset is bid up and the expensive one is sold down. That is why arbitrage links market efficiency to actual trading behavior.
Real-world frictions
Pure riskless arbitrage is rarer than textbooks suggest. Traders face transaction costs, funding constraints, settlement risk, regulatory barriers, and the possibility that “equivalent” payoffs are not truly identical. Those frictions explain why pricing gaps can persist.