规范不变性、几何和套利
Gauge Invariance, Geometry and Arbitrage
摘要：
在这项工作中，我们确定了最一般的措施，套利的任何市场模型由伊藤过程。我们证明了我们的套利测度在数值和等价概率的变化下是不变的。此外，这种测量具有作为规范连接的几何解释。该联络具有零曲率当且仅当没有套利。本文证明了鞅定价定理在套利情形下的一个推广。在我们的例子中，任何可交易资产的现值都是通过对未来现金流的期望值来给出的，该期望值是通过规范连接的线积分来贴现的。我们开发简单的策略来衡量套利使用模拟和真实的市场数据。我们发现，在我们有限的数据样本中，市场在一天或更长的时间范围内是有效的。然而，我们提供了强有力的证据，非零套利的高频日内数据。这样的事件似乎有一个衰减时间为一分钟的顺序。
英文摘要：
In this work, we identify the most general measure of arbitrage for any market model governed by Itô processes. We show that our arbitrage measure is invariant under changes of numéraire and equivalent probability. Moreover, such measure has a geometrical interpretation as a gauge connection. The connection has zero curvature if and only if there is no arbitrage. We prove an extension of the Martingale pricing theorem in the case of arbitrage. In our case, the present value of any traded asset is given by the expectation of future cash-flows discounted by a line integral of the gauge connection. We develop simple strategies to measure arbitrage using both simulated and real market data. We find that, within our limited data sample, the market is efficient at time horizons of one day or longer. However, we provide strong evidence for non-zero arbitrage in high frequency intraday data. Such events seem to have a decay time of the order of one minute.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
