arbitragefree

Arbitragefree refers to a market or model in which no arbitrage opportunities exist. An arbitrage opportunity is a self-financing trading strategy that requires no initial investment and yields a nonnegative payoff with positive probability of a strictly positive payoff. If such opportunities are absent, the market is considered arbitragefree or free of arbitrage.

In mathematical finance, the absence of arbitrage is closely tied to the existence of an equivalent martingale measure under which the discounted prices of traded assets are martingales. This connection is encapsulated in the Fundamental Theorem of Asset Pricing: a market is arbitragefree if and only if there exists an equivalent probability measure under which discounted asset prices form martingales. The theorem also highlights differences between complete and incomplete markets.

In complete markets, the martingale measure is unique, which yields a single arbitragefree price for any derivative. In incomplete markets, multiple equivalent martingale measures exist, leading to a range of arbitragefree prices. Pricing in this setting is often approached via hedging bounds or by selecting a particular measure that reflects risk preferences or model assumptions.

Practically, arbitragefree pricing computes the no-arbitrage price of contingent claims by taking the discounted expectation of their payoffs under a risk-neutral measure. If a market price lies outside the arbitragefree range, traders may exploit the discrepancy, or the discrepancy may be explained by market frictions such as transaction costs or liquidity constraints.

Notes and related concepts include the no-arbitrage condition, NFLVR (no free lunch with vanishing risk), and the broader framework of risk-neutral valuation and the fundamental theorem of asset pricing.