Wray Christopher M, Bishop Steven R
Department of Mathematics, University College London, London, United Kingdom.
PLoS One. 2016 Mar 23;11(3):e0151790. doi: 10.1371/journal.pone.0151790. eCollection 2016.
Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents' accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents' accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option.
金融市场中的羊群行为是一种反复出现的现象，它加剧了资产价格的波动，并被认为是导致市场脆弱性的一个可能因素。虽然有许多研究调查金融市场中的羊群行为，但通常在不考虑金融工具定价或其他市场动态的情况下进行。在此，基于存在信息阈值时的信息级联构建了一个交易者互动模型，以构建一个新的资产价格回报模型，该模型允许出现平静状态和类似羊群行为的状态。使用随机脉冲耦合网络对主体间的互动进行建模，该网络由信息阈值和网络耦合概率进行参数化。主体可能拥有一个或两个信息阈值，在每种情况下，这都决定了主体在进行交易之前可能占据的不同状态的数量。在主体拥有两个阈值的情况下（标记为有限状态空间模型，对应于主体在有界状态空间中积累信息），并且耦合强度最大时，推导出了级联规模概率的渐近表达式，并表明当达到网络耦合概率的临界值时，它遵循幂律。对于一系列模型参数，使用负二项分布的混合来近似级联规模分布。随后，这种近似被用于根据控制网络耦合概率的模型参数来表达模型价格回报的波动性。在主体拥有单个脉冲耦合阈值的情况下（标记为半无限状态空间模型，对应于主体在无界状态空间中积累信息），给出了数值证据，证明了资产回报波动性中的波动聚集和长期记忆模式。最后，将模型的输出与历史股票回报的分布以及股票指数期权的市场价格进行了比较。
