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on Market Microstructure |
| By: | Zhicheng Li; Haipeng Xing; Xinyun Chen |
| Abstract: | This paper studies inter-trade durations in the NASDAQ limit order market and finds that inter-trade durations in ultra-high frequency have two modes. One mode is to the order of approximately 10^{-4} seconds, and the other is to the order of 1 second. This phenomenon and other empirical evidence suggest that there are two regimes associated with the dynamics of inter-trade durations, and the regime switchings are driven by the changes of high-frequency traders (HFTs) between providing and taking liquidity. To find how the two modes depend on information in the limit order book (LOB), we propose a two-state multifactor regime-switching (MF-RSD) model for inter-trade durations, in which the probabilities transition matrices are time-varying and depend on some lagged LOB factors. The MF-RSD model has good in-sample fitness and the superior out-of-sample performance, compared with some benchmark duration models. Our findings of the effects of LOB factors on the inter-trade durations help to understand more about the high-frequency market microstructure. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1912.00764&r=all |
| By: | Antoine Fosset; Jean-Philippe Bouchaud; Michael Benzaquen |
| Abstract: | Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past volatility and price trends. Such a feedback mechanism inturn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects withina stylized order book model, we demonstrate numerically that there exists a second order phasetransition between a stable regime for weak feedback to an unstable regime for strong feedback,in which liquidity crises arise with probability one. We characterize the critical exponents, whichappear to belong to a new universality class. We then propose a simpler model for spread dynamicsthat maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for thereal markets, such a phase transition scenario requires the system to sit below, but very close tothe instability threshold (self-organised criticality), or else that the feedback intensity is itself timedependent and occasionally visits the unstable region. An alternative scenario is provided by a classof non-linear Hawkes process that show occasional "activated" liquidity crises, without having to bepoised at the edge of instability. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1912.00359&r=all |
| By: | Frédéric Bucci; Fabrizio Lillo; Jean-Philippe Bouchaud; Michael Benzaquen (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We revisit the trading invariance hypothesis recently proposed by Kyle and Obizhaeva [1] 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 R 2 > 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. |
| Date: | 2019–10–21 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02323318&r=all |
| By: | Ulrich Horst; Wei Xu |
| Abstract: | We provide a general probabilistic framework within which we establish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent Poisson random measures that capture the arrival of exogenous shocks and the arrival of self-excited shocks, respectively. Various well-studied stochastic volatility models with and without self-exciting price/volatility co-jumps are obtained as special cases under different scaling regimes. We analyze the impact of external shocks on the market dynamics, especially their impact on jump cascades and show in a mathematically rigorous manner that many small external shocks may tigger endogenous jump cascades in asset returns and stock price volatility. |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1911.12969&r=all |
| By: | Omar Euch (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique); Thibaut Mastrolia (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique); Mathieu Rosenbaum (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique); Nizar Touzi (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We address the mechanism design problem of an exchange setting suitable make-take fees to attract liquidity on its platform. Using a principal-agent approach, we provide the optimal compensation scheme of a market maker in quasi-explicit form. This contract depends essentially on the market maker inventory trajectory and on the volatility of the asset. We also provide the optimal quotes that should be displayed by the market maker. The simplicity of our formulas allows us to analyze in details the effects of optimal contracting with an exchange, compared to a situation without contract. We show in particular that it improves liquidity and reduces trading costs for investors. We extend our study to an oligopoly of symmetric exchanges and we study the impact of such common agency policy on the system. |
| Keywords: | financial regulation,market making,Make-take fees,stochastic control,principal-agent problem,high-frequency trading |
| Date: | 2019–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02379592&r=all |
| By: | L. C. Garcia Del Molino; I. Mastromatteo; Michael Benzaquen (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique); J.-P. Bouchaud |
| Abstract: | We reconsider the multivariate Kyle model in a risk-neutral setting with a single, perfectly informed rational insider and a rational competitive market maker, setting the price of n correlated securities. We prove the unicity of a symmetric, positive definite solution for the impact matrix and provide insights on its interpretation. We explore its implications from the perspective of empirical market microstructure, and argue that it provides a sensible inference procedure to cure some pathologies encountered in recent attempts to calibrate cross-impact matrices. |
| Date: | 2019–10–21 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02323433&r=all |