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In three bullet points: Efficiency: the obtained prices maximize assumed utilities of different agents. In their paper "The Valuation of Option Contracts and a Test of Market Efficiency", Cohen, Black and Scholes compare the theoretical value of options to their market price. The efficiency is in this sense: can agents obtain more or less in practice than ...


Lets look at generic markets with a single market filtration, then if $\mathbb{E}[S_t]=S_0$ then the market should be arbitrage free (absence of interest rates.) Otherwise there would be a butterfly arbitrage. But for more sophisticated markets, not at all. Consider a market where there are only is only one period and there are two agents, one who knows ...

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