NoArbitrage

No-arbitrage is a foundational principle in finance stating that in an efficient market there should be no opportunities to make a risk-free profit with zero net investment by exploiting price differences of the same asset or related assets across markets or times. When such opportunities exist, traders would act to lock in profits, and prices would adjust until the opportunity disappears.

Arbitrage strategies typically require no net investment and yield a risk-free payoff, such as buying underpriced assets while selling equivalent overpriced ones simultaneously. Examples include cash-and-carry trades, mispricing between futures and spot prices, or cross-market price discrepancies. In practice, real-world factors like transaction costs, liquidity constraints, and short-selling limits can limit or delay arbitrage.

In theoretical finance, the no-arbitrage condition underpins asset pricing. The Fundamental Theorem of Asset Pricing states that, in a frictionless market, absence of arbitrage is equivalent to the existence of an equivalent martingale (risk-neutral) measure; under this measure, discounted asset prices are martingales and derivative prices are given by risk-neutral expectations. In complete markets, this implies a unique arbitrage-free price for any contingent claim; in incomplete markets, prices form a range determined by the set of allowable martingale measures.

NFLVR, or no free lunch with vanishing risk, is a more rigorous formulation used in mathematical finance. Real markets include frictions such as transaction costs, taxes, and trading constraints, which can create or obscure apparent arbitrage. Overall, no-arbitrage remains a central concept for ensuring price consistency and enabling risk-neutral valuation.