# Latest Publications

## Beauty and structural complexity

S. Lakhal, A. Darmon, JP. Bouchaud, M. Benzaquen

15 Oct 2019

We revisit the long-standing question of the relation between image appreciation and its staistical properties. We generate two different sets of random images well distributed along three measures of entropic complexity. We run a large-scale survey un wich people are asked to sort the images by preference, wich reveals maximum appreciation at intermediate entropic complexity. We show tht the algorithmic complexity of the coarse-grained images, expected to capture structural complexity while abstracting from high frequency noise, is a good predictor of preferences. Our analysis suggets that there might exist some universal quantitative criteria for aesthetic judgement.

## Confidence Collapse in a Multi-Household, Self-Reflexive DSGE Model

F. Morelli, M. Benzaquen, M. Tarzia and J.-P. Bouchaud

17 Jul 2019

We investigate a multi-household DSGE model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich, and leads to a variety of realistic output dynamics: high output with no crises; high output with increased volatility and deep, short lived recessions; alternation of high and low output states where relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, narratives become an important monetary policy tool, that can help steering the economy back on track.

## Impact is not just volatility

F. Bucci, I. Mastromatteo, M. Benzaquen and J.-P. Bouchaud

5 Jul 2019

The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called “square-root impact law”, which states that impact grows as the square-root of traded volume, has nothing to do with price diffusion, i.e. that typical price changes grow as the square-root of time. We rationalise empirical findings on impact and volatility by introducing a simple scaling argument and confronting it to data.

## Are trading invariants really invariant? Trading costs matter

F. Bucci, F. Lillo, J.-P. Bouchaud and M. Benzaquen

12 Feb 2019

We revisit the trading invariance hypothesis recently proposed by Kyle and Obizhaeva by empirically investigating a large dataset of bets, or metaorders, provided by ANcerno. The hypothesis predicts that the quantity I := R/N^3/2, where R is the exchanged risk (volatility × volume × price) and N is the number of bets, is invariant. We find that the 3/2 scaling between R and N works well and is robust against changes of year, market capitalisation and economic sector. However our analysis clearly shows that I is not invariant. We find a very high correlation (> 0.8) between I and the total trading cost (spread and market impact) of the bet. We propose new invariants defined as a ratio of I and costs and find a large decrease in variance. We show that the small dispersion of the new invariants is mainly driven by (i) the scaling of the spread with the volatility per transaction, (ii) the near invariance of the distribution of metaorder size and of the volume and number fractions of bets across stocks.

## Slow decay of impact in equity markets: insights from the ANcerno database

F. Bucci, M. Benzaquen, F. Lillo, and J.-P. Bouchaud

17 janvier 2019

We present an empirical study of price reversion after the executed metaorders. We use a data set with more than 8 million metaorders executed by institutionalinvestors in the US equity market. We show that relaxation takes place as soonas the metaorder ends:while at the end of the same day it is on average ≈2/3 of the peak impact, the decay continues the next days, following a power-law functionat short time scales, and converges to a non-zero asymptotic value at long timescales (∼50 days) equal to ≈1/2 of the impact at the end of the first day. Dueto a significant, multiday correlation of the sign of executed metaorders, a carefuldeconvolution of theobservedimpact must be performed to extract the estimate ofthe impact decay of isolated metaorders.

## How does latent liquidity get revealed in the limit order book?

L. Dall'Amico*, A. Fosset*, J.-P. Bouchaud and M. Benzaquen

14 Nov 2018

Latent order book models have allowed for significant progress in our understanding of price formation in financial markets. In particular they are able to reproduce a number of stylized facts, such as the square-root impact law. An important question that is raised – if one is to bring such models closer to real market data – is that of the connection between the latent (unobservable) order book and the real (observable) order book. Here we suggest a simple, consistent mechanism for the revelation of latent liquidity that allows for quantitative estimation of the latent order book from real market data. We successfully confront our results to real order book data for over a hundred assets and discuss market stability. One of our key theoretical results is the existence of a market instability threshold, where the conversion of latent order becomes too slow, inducing liquidity crises.

## Crossover from Linear to Square-Root Market Impact

F. Bucci, M. Benzaquen, F. Lillo, and J.-P. Bouchaud

13 Nov 2018

Using a large database of 8 million institutional trades executed in the U.S. equity market, we establish a clear crossover between a linear market impact regime and a square-root regime as a function of the volume of the order. Our empirical results are remarkably well explained by a recently proposed dynamical theory of liquidity that makes specific predictions about the scaling function describing this crossover. Allowing at least two characteristic time scales for the liquidity (“fast” and “slow”) enables one to reach quantitative agreement with the data.

## Market impact with multi-timescale liquidity

M. Benzaquen and J.-P. Bouchaud

10 Oct 2017

We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we account for finite memory effects on the dynamics of the latent order book. We compute in particular the finite memory corrections to the square root impact law, as well as the impact decay and the permanent impact of a meta-order. The latter is found to be linear in the traded volume and independent of the trading rate, as dictated by no-arbitrage arguments. In addition, we consider the case of a spectrum of cancellation and deposition rates, which allows us to obtain a square root impact law for moderate participation rates, as observed empirically. Our multi-scale framework also provides an alternative solution to the so-called price diffusivity puzzle in the presence of a long-range correlated order flow.