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Register a new userAgent-based models for latent liquidity and concave price impact
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We revisit the epsilon-intelligence model of Toth et al.(2011), that was proposed as a minimal framework to understand the square-root dependence of the impact of meta-orders on volume in financial markets. The basic idea is that most of the daily liquidity is latent and furthermore vanishes linearly around the current price, as a consequence of the diffusion of the price itself. However, the numerical implementation of Toth et al. was criticised as being unrealistic, in particular because all the intelligence was conferred to market orders, while limit orders were passive and random. In this work, we study various alternative specifications of the model, for example allowing limit orders to react to the order flow, or changing the execution protocols. By and large, our study lends strong support to the idea that the square-root impact law is a very generic and robust property that requires very few ingredients to be valid. We also show that the transition from super-diffusion to sub-diffusion reported in Toth et al. is in fact a cross-over, but that the original model can be slightly altered in order to give rise to a genuine phase transition, which is of interest on its own. We finally propose a general theoretical framework to understand how a non-linear impact may appear even in the limit where the bias in the order flow is vanishingly small.
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We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the square-root impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.
We analyze a proprietary dataset of trades by a single asset manager, comparing their price impact with that of the trades of the rest of the market. In the context of a linear propagator model we find no significant difference between the two, suggesting that both the magnitude and time dependence of impact are universal in anonymous, electronic markets. This result is important as optimal execution policies often rely on propagators calibrated on anonymous data. We also find evidence that in the wake of a trade the order flow of other market participants first adds further copy-cat trades enhancing price impact on very short time scales. The induced order flow then quickly inverts, thereby contributing to impact decay.
We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity $g$) as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume $omega$ and $g$. The dependence on the volume (averaged over the granularity) of the Price Impact Surface is found to be a concave power law function $<phi(omega,g)>_gsimomega^delta$ with $deltaapprox 0.59$. Instead the dependence on the granularity is $phi(omega,g|omega)sim g^alpha$ with $alphaapprox-1$, showing a divergence of price fluctuations in the limit $gto 0$. Moreover, even in intermediate situations of finite liquidity, this effect can be very large and it is a natural candidate for understanding the origin of large price fluctuations.
We introduce a minimal Agent Based Model for financial markets to understand the nature and Self-Organization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a Random Walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The Stylized Facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effect which, however, can occur at different time scales. We propose a new mechanism for the Self-Organization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represent a crucial element for this state of Self-Organized-Intermittency. The model can be easily generalized to consider more realistic variants.
We introduce a minimal Agent Based Model with two classes of agents, fundamentalists (stabilizing) and chartists (destabilizing) and we focus on the essential features which can generate the stylized facts. This leads to a detailed understanding of the origin of fat tails and volatility clustering and we propose a mechanism for the self-organization of the market dynamics in the quasi-critical state. The stylized facts are shown to correspond to finite size effects which, however, can be active at different time scales. This implies that universality cannot be expected in describing these properties in terms of effective critical exponents. The introduction of a threshold in the agents action (small price fluctuations lead to no-action) triggers the self-organization towards the quasi-critical state. Non-stationarity in the number of active agents and in their action plays a fundamental role. The model can be easily generalized to more realistic variants in a systematic way.
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