ABSTRACT

The Kyle-Back Strategic Insider Trading is one of the most intriguing equilibrium models of asymmetric information in market microstructure theory, and has been studied extensively during the past 40 years. Many deep mathematical tools have been introduced to deal with the solvability issues, and touched many research areas form stochastic control, filtering, stochastic analysis, to optimal transports. A commonly known optimal strategy for the insider often has the “bridge” nature, which suggests that the insider trade super-aggressively before the asymmetric information exhausts, without taking in to account that such action might cause detection by the regulator, which could potentially lead to sever financial and criminal penalties. In this talk we consider a Kyle-type model where the insiders are aware of legal penalties and trying to “camouflage” their actions so as to strike a balance between expected wealth and the necessary stealth to avoid detection and subsequent prosecution. We establish the existence of an equilibrium for arbitrary population sizes as well as a unique liming equilibrium under mild conditions. A thorough convergence analysis provides key insights into the optimal scale of trading, determined by a “stealth index” by the insider, considering the population of liquidity traders. We show that the equilibrium can be closely approximated by a simply limit with minimal price impact. We also calibrate our model with two non-overlapping data sets spanning from 1980 to 2018, which underline the importance of stealth trading and the deterrent from both civil and criminal penalties. This talk is based on the joint work with Weixuan Xia and Jianfeng Zhang.