A Study of Future Markets and Stock Price Volatility Using Shannon's Separation Theorem

与市场交易有关的信息通常是外生和随机产生的。如果市场是有效的，这些市场“基本面”的给定样本必须在下一次样本出现之前可靠地传递给价格。市场连续出清的频率通常远远超过基本面的平均频率。基本面和市场出清价格之间的这种时间基础关系由通信通道共享，这些通信通道使用通道上的多次传输来传输单个信息源样本。但市场-渠道模拟是不完整的，因为市场主体的动机是利润，而渠道用户追求的是可靠的通信。这个提议表明，这些有时相互冲突的目标是可以解决的。这一建议的具体体现是，当市场代理在利润与可靠通信之间进行权衡时，一个流行的期货市场模型与一个具有无噪声反馈的通道上的带宽扩展模型是相同的。本文针对粮食期货市场提出了这种权衡的实证检验。该论证还表明，顺序拍卖模型作为信息来源的估计器，因此与股票估值模型中围绕价格波动的争议有关。研究通过比较源信息率和股票估值模型容量，估计公认的股票市场基本面的信息率，并建立波动率标准。所考虑的市场模型假设源信息是在随机时间爆发中产生的。因此，多交易者期货模型是一个多址信道源编码的研究。在具有最优获利回吐和最优信息传递这两个可检验假设的有效市场中，代理交易行为应该解决一个多址编码问题。市场理论中开放性问题的解决方案可以有助于沟通理论中的开放性问题，这进一步证明，确定知情市场参与者的比例解决了一个具有挑战性的问题，即寻找任意变化的渠道的容量。这项研究的意义在于，人们认识到，目前还没有已知的测试，可以对市场价格反映基本信息的最终可靠性给出标准衡量。成功的实证研究将建立这样一个标准。此外，将市场视为传播理论的共生体提供了一个前景，即实际市场可以作为解决传播理论中重大问题的实验资源。

Information relevant to market transactions is usually generated exogenously and at random times. A given sample of these market "fundamentals" must be reliably transmitted to prices before the next sample occurs if the market is to be efficient. Markets clear sequentially at a frequency which is typically far in excess of the average frequency of fundamentals. This time-base relation between fundamentals and market clearing prices is shared by communications channels which transmit individual information source samples using multiple transmissions on the channel. But the market-channel analog is incomplete because market agents are motivated by profits while channel users pursue reliable communication. This proposal suggests these sometimes conflicting goals can be resolved. The embodiment of the suggestion is a demonstration that a popular futures market model is identical to a model of bandwidth expansion over a channel with noiseless feedback when market agents tradeoff profits against reliable communication. Empirical tests of this tradeoff are proposed for a grain futures market. The demonstration also suggests that sequential auction models act as estimators of information sources and therefore are relevant to the controversy surrounding price volatility in stock valuation models. The research estimates information rates for recognized stock market fundamentals and establishes volatility standards by comparing source information rates with the stock valuation model capacity. The market models considered assume source information is generated in randomly timed bursts. Consequently, the multiple- trader futures model is a study in multiple-access channel source coding. In an efficient market with optimal profit-taking and information transfer, both testable hypotheses, agent trading behavior should solve a multiple-access coding problem. Tat solutions of pen problems in market theory can contribute to open problems in communication theory is further evidenced by showing that the determination of the proportion of informed market participants solves a challenging problem of finding the capacity of an arbitrarily varying channel. The significance of the study lies in the recognition that there are no known tests yielding a standard measure of the ultimate reliability with which market prices can reflect fundamental information. Successful empirical studies will establish such a standard. In addition, treating markets as a symbiont of communication theory offers the prospect that actual markets can serve as experimental resources for solving significant problems in communication theory.