Mini-Flash Crashes, Model Risk, and Optimal Execution

Abstract

Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision. We develop a mathematical model which captures aspects of these explanations. Empirical features of recent mini-flash crashes are present in our framework. For example, there are periods when no such events will occur. If they do, even just before their onset, market participants may not know with certainty that a disruption will unfold. Our miniflash crashes can materialize in both low and high trading volume environments and may be accompanied by a partial synchronization in order submission.Instead of adopting a classically-inspired equilibrium approach, we borrow ideas from the optimal execution literature. Each of our agents begins with beliefs about how his own trades impact prices and how prices would move in his absence. They, along with other market participants, then submit orders which are executed at a common venue. Naturally, this leads us to explicitly distinguish between how prices actually evolve and our agents' opinions. In particular, every agent's beliefs will be expressly incorrect.2010 Mathematics Subject Classification. Primary 91G80; Secondary 60H30, 60H10, 34M35.

Mean-Field Leader-Follower Games with Terminal State Constraint

“…Redistribution subject to SIAM license or copyright; see https://epubs.siam.org/terms-privacy the mean-field terms in [17,18] are exogenous (see [17, equation (3.16)] and [18, equation (3.11)]) while the mean-field term in our work is endogenous. Moreover, in [17,18] there are multiple groups of traders with heterogeneous beliefs (as in [7]),which is not the case in our model. The rest of this paper is organized as follows.…”

Asset pricing with heterogeneous beliefs and illiquidity

“…If all agents have equivalent beliefs, one could also consider heterogeneous holding costs as previously studied in models with homogeneous beliefs (Bouchard et al., 2018; Herdegen et al., 2019) or exogenous price dynamics (Bayraktar & Munk, 2018; Casgrain & Jaimungal, 2018). However, as in those studies, all agents' current positions would then appear as additional state variables and the system would become semilinear.…”

“…These are considered in Herdegen et al. (2019) for agents with homogeneous beliefs and in Bayraktar and Munk (2018) and Casgrain and Jaimungal (2018) for partial equilibrium models with heterogeneous beliefs.…”

Instabilities in Multi-Asset and Multi-Agent Market Impact Games

“…Furthermore, many works have recently examined the continuous time setting, e.g.,,Bayraktar and Munk (2018) and mean field games approach, e.g.,Cardaliaguet and Lehalle (2018),Fu et al (2021).…”