Market Impacts and the Life Cycle of Investors Orders

Abstract

In this paper, we use a database of around 400,000 metaorders issued by investors and electronically traded on European markets in 2010 in order to study market impact at different scales.At the intraday scale we confirm a square root temporary impact in the daily participation, and we shed light on a duration factor in 1/T γ with γ 0.25. Including this factor in the fits reinforces the square root shape of impact. We observe a power-law for the transient impact with an exponent between 0.5 (for long metaorders) and 0.8 (for shorter ones). Moreover we show that the market does not anticipate the size of the meta-orders. The intraday decay seems to exhibit two regimes (though hard to identify precisely): a "slow" regime right after the execution of the meta-order followed by a faster one. At the daily time scale, we show price moves after a metaorder can be split between realizations of expected returns that have triggered the investing decision and an idiosynchratic impact that slowly decays to zero.Moreover we propose a class of toy models based on Hawkes processes (the Hawkes Impact Models, HIM) to illustrate our reasoning. We show how the Impulsive-HIM model, despite its simplicity, embeds appealing features like transience and decay of impact. The latter is parametrized by a parameter C having a macroscopic interpretation: the ratio of contrarian reaction (i.e. impact decay) and of the "herding" reaction (i.e. impact amplification).

No‐arbitrage implies power‐law market impact and rough volatility

“…In Bacry, Iuga, et al. (2015), it is found that the market impact function fits a power‐law with exponent 0.45. In Gatheral et al.…”

“…Thus, there always exists a macroscopic PMI function and the convergence of the sequence is equivalent to that of . Motivated by the empirical results on market impact (Bacry, Iuga, et al., 2015; Bouchaud, 2010; Gomes & Waelbroeck, 2015; Lillo et al., 2003; Potters & Bouchaud, 2003) discussed in Section 1, we make the following natural assumption. Assumption For constant execution rate, that is for some , the scaling limit of the market impact function exists pointwise and is nonincreasing after time s .…”

“…The impact of a single order being very difficult to assess, one usually considers large sets of orders split by brokers, so‐called metaorders. Empirical studies of market impact have shown that for a buy metaorder (and symmetrically for a sell metaorder) market impact can be decomposed in two phases: a transient phase with a concave rise of the price during the metaorder execution, and a decay phase, where the price decreases toward a long‐term level after the execution is completed (see Bacry, Iuga, Lasnier, & Lehalle, 2015; Donier & Bonart, 2015; Lillo, Farmer, & Mantegna, 2003; Tóth et al., 2011).…”

“…As for the transient part of the market impact, empirical measurements show that provided the execution rate of the metaorder is relatively constant, the function is close to a power‐law with respect to time, that is with (see Bacry, Iuga, et al., 2015; Bouchaud, 2010; Lillo et al., 2003; Tóth et al., 2011). More precisely, the coefficient α is found to be about 1/2 so that the so‐called square root law is approximately satisfied.…”

Recurrent Poisson Process Unit for Speech Recognition

“…It is a random process whose realization consists of a sequence of isolated events with their time-stamps. Due to their generality, point processes have been widely used for modeling phenomena such as earthquakes (Hawkes 1971a), human activities (Malmgren et al 2008), financial data (Bacry et al 2015), context-aware recommendations (Du et al 2015), etc. A common property of the problems above is that the precise event time intervals can carry important information about the underlying dynamics, which otherwise are not available from the sequence of interval features that are evenly sampled from the continuous signal.…”