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Abstract: In this work, we identify the most general measure of arbitrage for anymarket model governed by It\^o processes. We show that our arbitrage measure isinvariant under changes of num\-{e}raire and equivalent probability. Moreover,such measure has a geometrical interpretation as a gauge connection. Theconnection has zero curvature if and only if there is no arbitrage. We prove anextension of the Martingale pricing theorem in the case of arbitrage. In ourcase, the present value of any traded asset is given by the expectation offuture cash-flows discounted by a line integral of the gauge connection. Wedevelop simple strategies to measure arbitrage using both simulated and realmarket data. We find that, within our limited data sample, the market isefficient at time horizons of one day or longer. However, we provide strongevidence for non-zero arbitrage in high frequency intraday data. Such eventsseem to have a decay time of the order of one minute.



Author: Samuel E. Vazquez, Simone Farinelli

Source: https://arxiv.org/







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