Agent-based models for latent liquidity and concave price impact

Abstract

We revisit the "ɛ-intelligence" model of Tóth et al. [Phys. Rev. X 1, 021006 (2011)], which 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 Tóth et al. (2011) was criticized 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 superdiffusion to subdiffusion reported in Tóth et al. (2011) is in fact a crossover 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 nonlinear impact may appear even in the limit where the bias in the order flow is vanishingly small.

A Million Metaorder Analysis of Market Impact on the Bitcoin

“…Thus, peak impact for the Bitcoin is consistent with the square-root law despite the prototypical nature of the Bitcoin market. This confirms the view expressed in Toth et al (2011a) and Mastromatteo et al (2014a) that market impact depends neither on microstructure (with e.g. arbitrage and high-frequency trading), nor on a clear metaorder distribution.…”

“…• The third class of models, initiated in a different context in Bak et al (1997), are statistical models of supply and demand (Donier et al 2015, Mastromatteo et al 2014a,b, Toth et al 2011a, that may also be seen as heterogeneous agents models (Donier and Bouchaud 2015a). The dynamics they give to the supply and demand that underlie the order book is such that both generically increase quadratically with distance from the mid-price, in turn leading to an exact and universal square-root impact at all scales.…”

“…Previous studies (Almgren et al 2005, Bershova and Rakhlin 2013, Gomes and Waelbroeck 2015, Mastromatteo et al 2014a, Moro et al 2009, Toth et al 2011a found that average market impact of a meta-order of total volume Q approximately follows the "square-root law",…”

Market Impact with Multi-Timescale Liquidity

“…(25) and (26), is rich enough to capture a large part of the subtleties of the dynamics of markets. It suggests an alternative framework to build agent based models of markets that generate realistic price series, that complement and maybe simplify previous attempts [7,9]. A remaining outstanding problem, however, is to reconcile the extended LLOB model proposed in this paper with some other well known "stylized facts" of financial price series, namely power-law distributed price jumps and clustered volatility.…”

Market Impacts and the Life Cycle of Investors Orders

“…The obtained model can then be used in an optimal trading scheme (see [Almgren et al, 2005a], [Gatheral, 2010] and [Lehalle and Dang, 2010] and for link with optimal trading see [Almgren and Chriss, 2000], [Gatheral and Schied, 2012] and [Bouchard et al, 2011]), or used by an investment firm to understand its trading costs (like in [Engle et al, 2012], [Bershova and Rakhlin, 2013], [Brokmann et al, 2014] or [Mastromatteo et al, 2013] written by author involved in investment firms).…”