arXiv subjects

Julien Kockelkoren

Publications and source records attributed to Julien Kockelkoren.

16 recordsLinked to original sources

arXiv2016

Agnostic Risk Parity: Taming Known and Unknown-Unknowns

Markowitz' celebrated optimal portfolio theory generally fails to deliver out-of-sample diversification. In this note, we propose a new portfolio construction strategy based on symmetry arguments only, leading to "Eigenrisk Parity" portfolios that achieve equal realized risk on all the principal components of the covariance matrix. This holds true for any other definition of uncorrelated factors. We then specialize our general formula to the most agnostic case where the indicators of future returns are assumed to be uncorrelated and of equal variance. This "Agnostic Risk Parity" (AGP) portfolio minimizes unknown-unknown risks generated by over-optimistic hedging of the different bets. AGP is shown to fare quite well when applied to standard technical strategies such as trend following.

q-fin.PM↗

arXiv2012

How does the market react to your order flow?

We present an empirical study of the intertwined behaviour of members in a financial market. Exploiting a database where the broker that initiates an order book event can be identified, we decompose the correlation and response functions into contributions coming from different market participants and study how their behaviour is interconnected. We find evidence that (1) brokers are very heterogeneous in liquidity provision -- some are consistently liquidity providers while others are consistently liquidity takers. (2) The behaviour of brokers is strongly conditioned on the actions of {\it other} brokers. In contrast brokers are only weakly influenced by the impact of their own previous orders. (3) The total impact of market orders is the result of a subtle compensation between the same broker pushing the price in one direction and the liquidity provision of other brokers pushing it in the opposite direction. These results enforce the picture of market dynamics being the result of the competition between heterogeneous participants interacting to form a complicated market ecology.

q-fin.TR↗

arXiv2011

Anomalous price impact and the critical nature of liquidity in financial markets

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.

q-fin.TR↗

arXiv2011

Models for the impact of all order book events

We propose a general framework to describe the impact of different events in the order book, that generalizes previous work on the impact of market orders. Two different modeling routes can be considered, which are equivalent when only market orders are taken into account. One model posits that each event type has a temporary impact (TIM). The "history dependent impact" model (HDIM), on the other hand, assumes that only price-changing events have a direct impact, itself modulated by the past history of all events through an "influence matrix" that measures how much, on average, an event of a given type affects the immediate impact of a price-changing event of the same sign in the future. We find in particular that aggressive market orders tend to reduce the impact of further aggressive market orders of the same sign (and increase the impact of aggressive market orders of opposite sign). We discuss the relative merits of TIM and HDIM, in particular concerning their ability to reproduce accurately the price diffusion pattern. We find that in spite of theoretical inconsistencies, TIM appears to fare better than HDIM when compared to empirical data. We ascribe this paradox to an uncontrolled approximation used to calibrate HDIMs, calling for further work on this issue.

q-fin.TR↗

arXiv2010

The price impact of order book events: market orders, limit orders and cancellations

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective impact on future price changes. We define and extract from the data the "bare" impact these events would have, if they were to happen in isolation. For large tick stocks, we show that a model where the bare impact of all events is permanent and non-fluctuating is in good agreement with the data. For small tick stocks, however, bare impacts must contain a history dependent part, reflecting the internal fluctuations of the order book. We show that this effect can be accurately described by an autoregressive model on the past order flow. This framework allows us to decompose the impact of an event into three parts: an instantaneous jump component, the modification of the future rates of the different events, and the modification of the future gaps behind the best quotes. We compare in detail the present formalism with the temporary impact model that was proposed earlier to describe the impact of market orders when other types of events are not observed. Finally, we extend the model to describe the dynamics of the bid-ask spread.

q-fin.TR↗

arXiv2007

Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets

We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid-ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility_per trade_, with R^2s exceeding 0.9. This correlation suggests both that the main determinant of the bid-ask spread is adverse selection, and that most of the volatilitycomes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the nyse, a liquid market with specialists, where monopoly rents appear to be present.

physics.data-an↗

arXiv2003

Absorbing Phase Transitions with Coupling to a Static Field and a Conservation Law

The coupling of branching-annihilating random walks to a static field with a local conservation law is shown to change the scaling properties of their phase transitions to absorbing states. In particular, we find that DP-class transitions give rise to a new universality class distinct from that characterizing the depinning of the so-called linear interface model.

cond-mat.stat-mech↗

arXiv2003

Phase field approach for modeling intracellular dynamics

We introduce a phase field approach for diffusion inside and outside a closed cell with damping and with source terms at the interface. The method is compared to exact solutions (where possible) and the more traditional finite element method. It is shown to be very accurate, easy to implement and computationally inexpensive. We apply our method to a recently introduced model for chemotaxis by Rappel et al. [Biophys. J. 83, 1361 (2002)].

cond-mat.stat-mech↗

arXiv2002

Late stages of coarsening in model C

We present a comprehensive picture of (non-critical) domain growth in model C systems where a non-conserved scalar order parameter is coupled to a conserved concentration field. For quenches into the region where the ordered and disordered phases coexist, we confirm earlier partial numerical results and find a growth exponent $z=3$. For quenches into the ordered region, we confirm the theoretical prediction $z=2$. Finally we discuss the implications of our results for domain growth in the microcanonical $ϕ^4$-model and we offer some criticism of the work of Somoza and Sagui on the morphology and wetting properties of domains.

cond-mat.stat-mech↗

arXiv2002

Comment on ``Deterministic equations of motion and phase ordering dynamics''

Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical $ϕ^4$ model displays unusual scaling laws. We show here, performing more careful numerical investigations, that Zheng only observed transient dynamics mostly due to the corrections to scaling introduced by lattice effects, and that Ising-like (model A) phase ordering actually takes place at late times. Moreover, we argue that energy conservation manifests itself in different corrections to scaling.

cond-mat.stat-mech↗

arXiv2002

Absorbing Phase Transitions of Branching-Annihilating Random Walks

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA --> (m+k)A, nA --> (n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of non-trivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair and triplet processes.

cond-mat.stat-mech↗

arXiv2001

Evidence for Slow Velocity Relaxation in Front Propagation in Rayleigh-Bénard Convection

Recent theoretical work has shown that so-called pulled fronts propagating into an unstable state always converge very slowly to their asymptotic speed and shape. In the the light of these predictions, we reanalyze earlier experiments by Fineberg and Steinberg on front propagation in a Rayleigh-Bénard cell. In contrast to the original interpretation, we argue that in the experiments the observed front velocities were some 15% below the asymptotic front speed and that this is in rough agreement with the predicted slow relaxation of the front speed for the time scales probed in the experiments. We also discuss the possible origin of the unusually large variation of the wavelength of the pattern generated by the front as a function of the dimensionless control parameter.

cond-mat↗

arXiv2000

Phase-ordering and persistence: relative effects of space-discretization, chaos, and anisotropy

The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (A. Lema\^ıtre & H. Chaté, {\em Phys. Rev. Lett.} {\bf 82}, 1140 (1999)) are revisited with the help of detailed investigations of interface motion. It is shown that ``normal'', curvature-driven-like domain growth is recovered at larger scales than considered before, and that the persistence exponent seems to be universal. Using generalized persistence spectra, the properties of interface motion in this deterministic, chaotic, lattice system are found to ``interpolate'' between those of the two canonical reference systems, the (probabilistic) Ising model, and the (deterministic), space-continuous, time-dependent Ginzburg-Landau equation.

cond-mat.stat-mech↗

arXiv2000

Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''

Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999), cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional systems of sequentially-updated chaotic maps with conserved ``order parameter'' does not belong, for large regions of parameter space, to the expected universality class. We show here that these results are due to a slow crossover and that a careful treatment of the data yields normal dynamical scaling. Moreover, we construct better models, i.e. synchronously-updated coupled map lattices, which are exempt from these crossover effects, and allow for the first precise estimates of persistence exponents in this case.

cond-mat↗

arXiv1999

Fixed points, stability and intermittency in a shell model for advection of passive scalars

We investigate the fixed points of a shell model for the turbulent advection of passive scalars introduced Jensen, Paladin and Vulpiani. The passive scalar field is driven by the velocity field of the popular GOY shell model. The scaling behavior of the static solutions is found to differ significantly from Obukhov-Corrsin scaling theta_n ~ k_n^(-1/3) which is only recovered in the limit where the diffusivity vanishes, D -> 0. From the eigenvalue spectrum we show that any perturbation in the scalar will always damp out, i.e. the eigenvalues of the scalar are negative and are decoupled from the eigenvalues of the velocity. Furthermore we estimate Lyapunov exponents and the intermittency parameters using a definition proposed by Benzi et al. The full model is as chaotic as the GOY model, measured by the maximal Lyapunov exponent, but is more intermittent.

chao-dyn↗

arXiv1998

Chaotic Behavior in Shell Models and Shell Maps

We study the chaotic behavior of the ``GOY'' shell model by measuring the variation of the maximal Lyapunov exponent with the parameter $ε$ which determines the nature of the second invariant (the generalized ``helicity'' invariant). After a Hopf bifurcation, we observe a critical point at $ε_c \sim 0.38704$ above which the maximal Lyapunov exponent grows nearly linearly. For high values of $ε$ the evolution becomes regular again which can be explained by a simple analytic argument. A model with few shells shows two transitions. To simplify the model substantially we introduce a shell map which exhibits similar properties as the``GOY'' model.

chao-dyn↗