Market Efficiency, No-Arbitrage, and Equilibrium in Pricing
Summary
The document compares three ideas used to explain why the Black–Scholes–Merton option-pricing formula can hold: profitable trading opportunities, market efficiency, and market equilibrium. It asks why equilibrium might be considered the most important of these explanations. The response distinguishes the concepts by their scope and assumptions.
No-arbitrage is described as a local, objective opportunity to buy and sell at inconsistent prices, without requiring a utility model. Efficiency concerns an individual agent optimizing according to a specified utility. Equilibrium is broader: it describes a market in which participants are simultaneously optimizing and have expectations about how others behave. The passage offers these conceptual distinctions but does not derive the pricing formula or establish that one framework is universally superior; the claim about equilibrium’s importance is presented through a cited discussion rather than supporting analysis.
Key ideas
- No-arbitrage identifies price inconsistencies that can be exploited without specifying an agent’s utility.
- Market efficiency is framed around an individual agent optimizing a quantified utility.
- Market equilibrium is a global condition involving simultaneous optimization across participants.
- The document compares explanatory frameworks for option pricing but does not prove one is universally best.
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Full text
# What is the difference between market efficiency, market equilibrium, and no-arbitrage? # What is the difference between market efficiency, market equilibrium, and no-arbitrage? Aaron Brown (in the book, The Poker Face of Wall Street, p. 196), discusses four approaches to deriving the same Black-Scholes-Merton option-pricing formula: > Ed Thorp, Myron Scholes, Robert Merton, and Fischer Black all had almost the same formula [for option-pricing], but each had a different reason for believing it was true. Ed showed that it was a way to make money, Scholes that it was required for market efficiency, Merton that it had to be true or there would be arbitrage, and Black that it was required for market equilibrium. Black's insight turned out to be the most important... What is the difference between "market efficiency", "no arbitrage", and "market equilibrium", and why would equilibrium be considered the most important insight? ## Answer by lehalle (score 6) https://quant.stackexchange.com/a/15396 In three bullet points: To compare the three concepts: - an agent does not need to have a utility function to implement arbitrage, it is a very local and objective behaviour: observe prices, buy low and sell high... - efficiency is to be optimal for one agent. That for he needs to objective and quantify his utility and maximize it. It means the considered agent is rational an advanced way. - last but not least: market equilibrium. It is a global property: everyone is optimal simultaneously, and knows others are optimal (and know how they manage to be).
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