论文标题
股票市场的集体回报动力学中的新兴不变性和扩展性能
Emergent invariance and scaling properties in the collective return dynamics of a stock market
论文作者
论文摘要
几项作品在不同市场的回报分布中观察到了重尾行为，这是基本复杂动态的可观察到的指标。这种先前的工作研究回报分布在市场上的各个股票中都被边缘化，并且没有跟踪有关以不同股票为条件的收益的共同分配的统计数据，这对于优化储备间资产分配策略非常有用。作为朝着这一目标的一步，我们研究了其成对相关性捕获的回报分布中的新兴现象。特别是，我们考虑对市场模式的收益的部分相关（$ c_ {i，j}（τ）（τ）$（因此，在不同的时间范围内的基线回报行为），在不同的时间范围内（$τ$），并发现两个新颖的现象：（i）$ c_（I）， $τ$不变，从$ 1000 \ textrm {min} $（2.5天）到$ 30000 \ textrm {min} $（2.5个月）； （ii）$ c_ {i，j}（τ）$的标准偏差的缩放在此制度内接受\ iffalse，在经验上可以\ fi \ fi非常适合简单的模型类，例如powerlaw $ $τ^{ - λ} $或伸展的指向expectext opperted offectential offected offected offectent offect offectept offectept offectect of tumpartect of topparifect $ e e^^$ e e e e e e e e e e e e e e^=^$）此外，管理这些拟合的参数提供了市场健康的摘要视图：例如，在以前所未有的金融危机为标志的几年中，例如2008美元$和2020美元 - 值$λ$（缩放指数）的价值大大降低。最后，我们证明，现有的生成框架（例如单因素模型）无法充分支持所观察到的紧急行为。我们介绍了一个有前途的基于代理的Vicsek模型，该模型缩小了这一差距。
Several works have observed heavy-tailed behavior in the distributions of returns in different markets, which are observable indicators of underlying complex dynamics. Such prior works study return distributions that are marginalized across the individual stocks in the market, and do not track statistics about the joint distributions of returns conditioned on different stocks, which would be useful for optimizing inter-stock asset allocation strategies. As a step towards this goal, we study emergent phenomena in the distributions of returns as captured by their pairwise correlations. In particular, we consider the pairwise (between stocks $i,j$) partial correlations of returns with respect to the market mode, $c_{i,j}(τ)$, (thus, correcting for the baseline return behavior of the market), over different time horizons ($τ$), and discover two novel emergent phenomena: (i) the standardized distributions of the $c_{i,j}(τ)$'s are observed to be invariant of $τ$ ranging from from $1000 \textrm{min}$ (2.5 days) to $30000 \textrm{min}$ (2.5 months); (ii) the scaling of the standard deviation of $c_{i,j}(τ)$'s with $τ$ admits \iffalse within this regime is empirically observed to \fi good fits to simple model classes such as a power-law $τ^{-λ}$ or stretched exponential function $e^{-τ^β}$ ($λ,β> 0$). Moreover, the parameters governing these fits provide a summary view of market health: for instance, in years marked by unprecedented financial crises -- for example $2008$ and $2020$ -- values of $λ$ (scaling exponent) are substantially lower. Finally, we demonstrate that the observed emergent behavior cannot be adequately supported by existing generative frameworks such as single- and multi-factor models. We introduce a promising agent-based Vicsek model that closes this gap.
