论文标题
知情交易,限制订单簿和实施不足:平衡和渐近学
Informed trading, limit order book and implementation shortfall: equilibrium and asymptotics
论文作者
论文摘要
我们为限制订单簿提出了一个静态平衡模型,其中利润最大化的投资者会收到有关资产清算价值的信息信号,并通过具有随机初始库存的竞争经销商执行,该库存随机初始库存,后者与流动性供应商所填补的竞争性限制订单书进行交易。我们表明,存在一个有界信号分布的平衡,获得了Bernoulli-Type信号的封闭形式解,并提出了一种直接的迭代算法,以计算一般情况的平衡订单簿。我们为大型行业的市场影响获得了确切的分析渐近学,并表明功能形式取决于内部人员的私人信号的尾巴分布。特别是,如果信号具有脂肪尾巴,则在法律较轻的情况下具有对数时,就会遵循功率定律。此外,平衡中贸易量的尾巴分布遵守我们模型中的权力定律。我们发现,流动性供应商收取的最低出价差距与“噪声”交易的数量无关,但在均衡中内部人员的信息优势的程度增加。该模型还预测,随着噪声交易的数量增加与成比例交易成本的模型的融合。内部人员之间的竞争会导致积极交易,从而导致总利润在限制案例$ n \至\ infty $中消失。数值结果还表明,随着内部人员的数量,将其他参数固定的数量增加。最后,如果清算值无限制,则可能不存在平衡。我们猜想,如果信号分布表现出脂肪尾巴,则存在平衡需要足够的内部人群竞争。
We propose a static equilibrium model for limit order book where profit-maximizing investors receive an information signal regarding the liquidation value of the asset and execute via a competitive dealer with random initial inventory, who trades against a competitive limit order book populated by liquidity suppliers. We show that an equilibrium exists for bounded signal distributions, obtain closed form solutions for Bernoulli-type signals and propose a straightforward iterative algorithm to compute the equilibrium order book for the general case. We obtain the exact analytic asymptotics for the market impact of large trades and show that the functional form depends on the tail distribution of the private signal of the insiders. In particular, the impact follows a power law if the signal has fat tails while the law is logarithmic in case of lighter tails. Moreover, the tail distribution of the trade volume in equilibrium obeys a power law in our model. We find that the liquidity suppliers charge a minimum bid-ask spread that is independent of the amount of `noise' trading but increasing in the degree of informational advantage of insiders in equilibrium. The model also predicts that the order book flattens as the amount of noise trading increases converging to a model with proportional transactions costs.. Competition among the insiders leads to aggressive trading causing the aggregate profit to vanish in the limiting case $N\to\infty$. The numerical results also show that the spread increases with the number of insiders keeping the other parameters fixed. Finally, an equilibrium may not exist if the liquidation value is unbounded. We conjecture that existence of equilibrium requires a sufficient amount of competition among insiders if the signal distribution exhibit fat tails.