Encyclopedia of Financial Models I

Arbitrage Pricing: Finite-State Models

SERGIO M. FOCARDI, PhD

Partner, The Intertek Group

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: Arbitrage in its most basic form involves the simultaneous buying and selling of an asset at two different prices in two different markets. In real-world financial markets, arbitrage opportunities rarely, if ever, exist. Less obvious arbitrage opportunities exist in situations where a package of assets can be assembled that have a payoff (return) that is identical to an asset that is priced differently. A market is said to be a complete market if an arbitrary payoff can be replicated by a portfolio. The most fundamental principle in asset pricing theory is the absence of arbitrage opportunities.

The principle of absence of arbitrage or the no-arbitrage principle is perhaps the most fundamental principle of finance theory. In the presence of arbitrage opportunities, there is no trade-off between risk and returns because it is possible to make unbounded risk-free gains. The principle of absence of arbitrage is fundamental for understanding asset valuation in a competitive market. This entry discusses arbitrage pricing in a finite-state, discrete-time setting. However, it is important to note that there are well-known limits to arbitrage, first identified by Shleifer and Vishny (1997), resulting from restrictions imposed on rational traders and, as a result, pricing inefficiencies may exist for a period ...