摘要翻译：
我们建立了一个简单的带有保证金通知的杠杆资产购买模型。投资基金使用的可能是最基本的金融策略，称为“价值投资”，即有系统地试图购买被低估的资产。当资金不借入时，资产的价格波动是正态分布的，跨时间不相关。当这些资金被允许杠杆化，即从银行借款，以购买超过其财富允许的更多资产时，所有这些都发生了变化。在好的时候，竞争促使投资者选择使用更多杠杆的基金，因为它们有更高的利润。随着杠杆率的增加，价格波动变得严重，并显示出集群波动，类似于在实际市场中观察到的情况。以前对肥尾和集群波动性的解释依赖于“非理性行为”，如趋势跟随。相反，这来自于这样一个事实，即杠杆限制导致基金在下跌的市场中抛售：谨慎的银行通过设定杠杆限制，使自己在当地更加安全，因此当一只基金超过杠杆限制时，它必须通过出售资产来部分偿还贷款。不幸的是，当价格已经下跌时，这有时会同时发生在所有基金身上。由此产生的非线性反馈放大了价格的大幅下行。在极端情况下，这会导致崩溃，但这种影响在每一个时间尺度上都可以看到，产生价格扰动的幂律。一种标准的（应该是更复杂的）风险控制政策，在这种政策中，个别银行将杠杆限制建立在波动性基础上，导致杠杆在波动性低的时期上升，在波动性高的时候收缩得更快，使这些极端的波动变得更加严重。
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英文标题：
《Leverage Causes Fat Tails and Clustered Volatility》
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作者：
Stefan Thurner, J. Doyne Farmer, John Geanakoplos
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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英文摘要：
  We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing", i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior", such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.
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PDF链接：
https://arxiv.org/pdf/0908.1555