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摘要翻译：
通过响应函数等动态量，研究了具有买卖价差的订单驱动双拍卖市场的统计性质。我们首先尝试利用所谓的{Madhavan-Richardson-Roomans模型}（简称MRR）来模拟经验数据集（如EUR/JPY或USD/JPY汇率）中买卖价差随时间波动的价格变化随机过程。我们发现MRR理论显然不能模拟从数据中计算出的响应函数$R(l)$($l$表示响应函数被评估的时间差异）的定性行为('非单调‘行为）。特别地，我们证实了买卖价差的随机性使$R(l)$与自相关函数$C(l)$之间的线性关系明显偏离，即$R(l)\propto-C(l)$。为了建立具有随机买卖价差的双重拍卖市场的微观模型，我们使用了具有有限市场历史长度的少数人博弈，从数值上发现博弈的适当扩展表现出与经验证据相当相似的响应函数行为。我们还揭示了使用自适应（退火）查找表的少数博弈模型比固定（淬火）查找表更有效地再现了非线性关系$R(l)\propto-F(C(l))$($F(x)$代表一个导致“$\lambda$-shapes”）的非线性函数。
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英文标题：
《Response of double-auction markets to instantaneous Selling-Buying
signals with stochastic Bid-Ask spread》
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作者：
Takero Ibuki, Jun-ichi Inoue
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最新提交年份：
2011
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分类信息：
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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一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
Statistical properties of order-driven double-auction markets with Bid-Ask spread are investigated through the dynamical quantities such as response function. We first attempt to utilize the so-called {\it Madhavan-Richardson-Roomans model} (MRR for short) to simulate the stochastic process of the price-change in empirical data sets (say, EUR/JPY or USD/JPY exchange rates) in which the Bid-Ask spread fluctuates in time. We find that the MRR theory apparently fails to simulate so much as the qualitative behaviour ('non-monotonic' behaviour) of the response function $R(l)$ ($l$ denotes the difference of times at which the response function is evaluated) calculated from the data. Especially, we confirm that the stochastic nature of the Bid-Ask spread causes apparent deviations from a linear relationship between the $R(l)$ and the auto-correlation function $C(l)$, namely, $R(l) \propto -C(l)$. To make the microscopic model of double-auction markets having stochastic Bid-Ask spread, we use the minority game with a finite market history length and find numerically that appropriate extension of the game shows quite similar behaviour of the response function to the empirical evidence. We also reveal that the minority game modeling with the adaptive ('annealed') look-up table reproduces the non-linear relationship $R(l) \propto -f(C(l))$ ($f(x)$ stands for a non-linear function leading to '$\lambda$-shapes') more effectively than the fixed (`quenched') look-up table does.
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PDF链接：
https://arxiv.org/pdf/1011.0748
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