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on Market Microstructure |
| By: | Nicolas Baradel (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique, ENSAE - Ecole Nationale de la Statistique et de l'Analyse Economique - Ecole Nationale de la Statistique et de l'Analyse Economique); Bruno Bouchard (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique, PSL - PSL Research University); David Evangelista (KAUST - King Abdullah University of Science and Technology); Othmane Mounjid (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [14, 20, 21], the MM and the HFT define their trading strategy by optimizing the expected utility of terminal wealth, while the IB has a prescheduled task to sell or buy many shares of the considered asset. We derive the variational partial differential equations that characterize the value functions of the MM and HFT and explain how almost optimal control can be deduced from them. We then provide a first illustration of the interactions that can take place between these different market participants by simulating the dynamic of an order book in which each of them plays his own (optimal) strategy. |
| Keywords: | Optimal trading,Market impact,Optimal control |
| Date: | 2018–02–15 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01710301&r=mst |
| By: | Mathias Pohl; Alexander Ristig; Walter Schachermayer; Ludovic Tangpi |
| Abstract: | Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades $N$, and traded volume $V$ in the asset, its price $P$, the squared volatility $\sigma^2$, the corresponding bid-ask spread $S$ and the cost of trading $C$. Different reasonings result in simple proportionality relations ("scaling laws") between these variables. A basic proportionality is established between the trading activity and the squared volatility, i.e., $N \sim \sigma^2$. More sophisticated relations are the so called 3/2-law $N^{3/2} \sim \sigma P V /C$ and the intriguing scaling $N \sim (\sigma P/S)^2$. We prove that these "scaling laws" are the only possible relations for considered sets of variables by means of a well-known argument from physics: dimensional analysis. Moreover, we provide empirical evidence based on data from the NASDAQ stock exchange showing that the sophisticated relations hold with a certain degree of universality. Finally, we discuss the time scaling of the volatility $\sigma$, which turns out to be more subtle than one might naively expect. |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1803.04892&r=mst |
| By: | Venky Venkateswaran (New York University); Ariel Zetlin-Jones (Carnegie Mellon University); Ali Shourideh (Carnegie Mellon University); Benjamin Lester (Federal Reserve Bank of Philadelphia) |
| Abstract: | We study a dynamic financial market where informed traders meet and trade with marketmakers in bilateral interactions. In such an environment, market liquidity, summarized by the bid-ask spread, is determined jointly by the two primitive forces, namely search frictions (as in Duffie et. al., 2005) and asymmetric information (in the spirit of Glosten and Milgrom, 1985). We show that their interaction leads to novel and perhaps surprising implications, both positive and normative. Reducing trading frictions, for example, leads to a decline in the speed of learning from market-wide activities. This in turn exacerbates the effects of asymmetric information, which can lead to lower liquidity and welfare. On the other hand, more transparency increases the distortions from market-power and also has negative liquidity/welfare consequences. Finally, we devise an empirical strategy to disentangle the significance of each friction from observable data on trades. Our results point to the value of a unified framework with both frictions for evaluating the effects of policies. |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:red:sed017:1554&r=mst |
| By: | Rui Fan (School of Management, Swansea University); Oleksandr Talavera (School of Management, Swansea University); Vu Tran (School of Management, Swansea University) |
| Abstract: | This study examines whether stock indicators are affected by information in social media such as Twitter. Using a daily sample of tweets with a FTSE 100 firm name over two years, we find insignificant associations between tweets/bot-tweets and stock returns whereas there is a strongly significant association with volatility and trading volume. Using a high-frequency sample, we detect a positive (negative) impact of tweets (bot-tweets) on stock returns. The impact of bot-tweets vanishes within 30 minutes. The results for volatility and trading volume are consistent with the daily data analysis. In addition, event study reveals a bounce-back pattern of price reactions in response to negative retweets. Abnormal increases in tweets/bottweets have significant effects on stock volatility, trading volume and liquidity. |
| Keywords: | Social media bots, investor sentiments, noise traders, text classification, computational linguistics |
| JEL: | G12 G14 L86 |
| Date: | 2018–03–23 |
| URL: | http://d.repec.org/n?u=RePEc:swn:wpaper:2018-30&r=mst |
| By: | Giuseppe Buccheri; Giacomo Bormetti; Fulvio Corsi; Fabrizio Lillo |
| Abstract: | We propose a new multivariate conditional correlation model able to deal with data featuring both observational noise and asynchronicity. When modelling high-frequency multivariate financial time-series, the presence of both problems and the requirement for positive-definite estimates makes the estimation and forecast of the intraday dynamics of conditional covariance matrices particularly difficult. Our approach tackles all these challenging tasks within a new Gaussian state-space model with score-driven time-varying parameters that can be estimated using standard maximum likelihood methods. Similarly to DCC models, large dimensionality is handled by separating the estimation of correlations from individual volatilities. As an interesting outcome of this approach, intra-day patterns are recovered without the need of any cross-sectional averaging, allowing, for instance, to estimate the real-time response of the market covariances to macro-news announcements. |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1803.04894&r=mst |
| By: | Tetsuji Okazaki (Faculty of Economics, University of Tokyo) |
| Abstract: | This paper explores the modes of trading of a trading company and their implications on the risks and returns of trades, focusing on Mitsubishi Corporation in the 1920s. Mitsubishi employed two modes of trades, i.e. proprietary trading and consignment trading, and the former trades accounted for 43.8% of the total trades in 1928. From the original account book of Mitsubishi, I compiled a dataset containing the information of sales and margins at the individual transaction-level. It is revealed that there is substantial difference in the distributions of margin rates between proprietary trading and consignment trading. The distribution of margin rates of the proprietary trading has fat tails both on the left and right sides, and the average margin rate is significantly higher than that of consignment trades. As expected, proprietary trading yielded high risk and high return. The findings of this paper suggests further issues to be explored, including the choice of modes of trading by Mitsubishi and the mechanisms that Mitsubishi controlled the risk accompanying transactions by its own account. |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:tky:jseres:2016cj282&r=mst |
| By: | Ismael Lemhadri (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We revisit the classical problem of market impact through the lens of a new agent-based model. Drawing from the mean-field approach in Statistical Mechanics and Physics, we assume a large number of 'agents' interacting in the order book. By taking the 'continuum' limit we obtain a set of nonlinear differential equations, the core of our dynamical theory of price formation. And we explicitly solve them using Fourier analysis. One could talk as well of a "micro-macro" approach of equilibrium, where the market price is the consequence of each ("microscopic") agent behaving with respect to his preferences and to global ("macroscopic") information. When a large market order (or "metaorder") perturbs the market, our model recovers the square-root law of impact, providing new insights on the price formation process. In addition, we give various limiting cases, examples and possible extensions. |
| Keywords: | mean-eld games,market microstructure,optimal execution strategies,reaction- diusion,agent-based models,latent order book,price formation,market impact |
| Date: | 2018–02–16 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01711192&r=mst |
| By: | Philippe Casgrain; Sebastian Jaimungal |
| Abstract: | Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform statistical arbitrage, where all agents filter the latent states of the world, and their trading actions have permanent and temporary price impact. This leads to a large stochastic game with heterogeneous agents. We solve the stochastic game by investigating its mean-field game (MFG) limit, with sub-populations of heterogenous agents, and, using a convex analysis approach, we show that the solution is characterized by a vector-valued forward-backward stochastic differential equation (FBSDE). We demonstrate that the FBSDE admits a unique solution, obtain it in closed-form, and characterize the optimal behaviour of the agents in the MFG equilibrium. Moreover, we prove the MFG equilibrium provides an $\epsilon$-Nash equilibrium for the finite player game. We conclude by illustrating the behaviour of agents using the optimal MFG strategy through simulated examples. |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1803.04094&r=mst |