Self-organised criticality in high frequency finance: the case of flash crashes

High frequency trading and the dynamics of market microstructure have seen growing interest in both academia and industry, with the rise of electronic trading and the emergence of major HFT market makers in recent years. Electronic trading has led to an increase in trading volumes and frequencies particularly in the last decade, which sparked an investigation into how market dynamics have evolved with market players. The literature and practitioners alike have noted that price efficiency has improved as a result, but also that exchanges, assets and even markets now carry more systemic risk as a result of large players covering the whole space with similar methods and risk constraints shared across assets and exchanges. The growth in systemic risk due to electronic trading has given rise to a growing number of increasingly large flash crashes (1) of which the one of May 6th 2010 was the first notorious example. The report on the May 6th crash by Nanex (2) begins to suggest how high frequency order placement and saturation might have worsened the extent of the crash. The authors in (3) delve deeper into this idea and investigate flash crashes between 2006 and 2011 to show a system-wide phase transition around ∼ 500ms to an all-electronic trading market characterised by black swan events. Further insight into the impact of HFT players in flash crashes was provided by the simulations in (4), where the authors show how lowering the number of HFT players in the simulation reduces the extent of the crash, even when the size of the large sell order which triggered it is kept constant. The authors explain the relation between the number of HFT players and the extent of the crash as due to the “hot potato” phenomenon described in (5). This phenomenon can be explained as follows. When an unusually large sell (buy) order hits the market it gets absorbed by liquidity providers (often HFT market makers) which, as a result, accumulate a short position in their inventory. The unusually large order though impacts the price and potentially triggers risk limits by those market makers holding the inventory. Meanwhile as the price drops (rises) dramatically ordinary market players withdraw from the market. As a result of the risk limits HFTs try to reduce their inventory with aggressive market orders. As everyone else has withdrawn, they trade with each other at extremely high frequency, thereby creating high trading volumes. This particular phase characterises the “hot potato” phenomenon, i.e. the inventory exposure being passed around like a “hot potato”. The positive feedback loop continues as follows. When trading volume is used as a proxy for liquidity the “hot potato” phenomenon creates apparent liquidity which triggers execution by lower frequency players which are also trying to reduce exposure as the market drops. The authors in (5) make two further points on HFTs and modern market dynamics during these extreme events. Another cause of apparent liquidity and market depth is fleeing liquidity by HFT market makers. The fast cancellation of limit orders has been the extensive topic of discussion and was suggested to create the illusion of market depth with the consequences discussed above. As the number of trading venues and exchanges rises liquidity is fragmented. Sweep orders and arbitrageurs aim to move liquidity and remove arbitrage opportunities across exchanges, but can create dangerous effects. Sweep orders between markets operate at lower frequencies than these fast cancellations, thereby sweeping the book after liquidity has potentially already been removed. This worsens the systemic aspect of these events across the fragmented liquidity structure of exchanges. Extreme events of this kind, which are characterised by non-linear reactions to shocks in the system and positive feedback loops, exist in man-made and natural systems and are instances of self-organised criticality. In this type of systemic events the system reaches a critical state where a small release in energy or imbalance triggers highly non-linear reactions in size. This is the case of avalanches and more, as described in (6). Events with such underlying dynamics are characterised by heavy-tailed and in particular power law distributions. The tail’s decay exponent in these distributions is crucial for their modeling as it indicates which moments of the distribution are defined and which diverge. This can be of great practical relevance for both regulators and practitioners, in particular market makers. These are market players with an obligation to provide liquidity at all times, such as banks, which cannot simply withdraw from the market under extreme conditions, but must continue to provide prices for their clients to trade at. This constraint brings the need to model trade volume flow