Arbitrage
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
A trading strategy that requires no net investment, carries no risk of loss, and has a positive probability of gain. The assumption that arbitrage opportunities do not persist is the foundation of derivatives pricing.
Arbitrage in plain English
Arbitrage is the finance version of a free lunch: a way to lock in a profit that costs you nothing upfront and can never lose money, while sometimes paying off. Imagine the same trading card selling for $10 at one shop and $12 at the shop next door — you could buy low, instantly sell high, and pocket the difference with zero risk. In real markets these gaps get spotted and traded away almost instantly, so we assume they don't stick around. That single assumption — that free lunches vanish fast — is the bedrock the entire pricing of options and other derivatives is built on.
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