投机与幂律
Speculation and Power Law
摘要：
金融价格的变化是按照三次指数的幂律分布的。这是一个令人着迷的规律，因为它适用于不同市场、不同时间尺度的不同类别的证券。这一规律的普适性意味着其背后必然存在某种基本的、普遍的、稳定的机制，而标准范式（新古典范式）则不存在这种机制。另一方面，基于主体的金融市场模型展示了真实的价格变化，但它们涉及相对复杂的、往往在数学上难以处理的机制。本文指出了幂律背后的一个简单原理：投机思想本身所固有的反馈，即在预期价格上涨时买入（在预期价格下跌时卖出）。通过这种反馈，价格变化遵循随机系数自回归过程，因此它们具有凯斯滕定理的幂律。
英文摘要：
It is now well established empirically that financial price changes are distributed according to a power law, with cubic exponent. This is a fascinating regularity, as it holds for various classes of securities, on various markets, and on various time scales. The universality of this law suggests that there must be some basic, general and stable mechanism behind it. The standard (neoclassical) paradigm implies no such mechanism. Agent-based models of financial markets, on the other hand, exhibit realistic price changes, but they involve relatively complicated, and often mathematically intractable, mechanisms. This paper identifies a simple principle behind the power law: the feedback intrinsic to the very idea of speculation, namely buying when one expects a price rise (and selling when one expects a price fall). By this feedback, price changes follow a random coefficient autoregressive process, and therefore they have a power law by Kesten theorem.
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