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on Market Microstructure |
| By: | Pietro Fodra (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie (UPMC) - Paris VI - Université Paris VII - Paris Diderot); Huyen Pham (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie (UPMC) - Paris VI - Université Paris VII - Paris Diderot) |
| Abstract: | We study an optimal high frequency trading problem within a market microstructure model aiming at a good compromise between accuracy and tractability. The stock price is modeled by a Markov Renewal Process (MRP), while market orders arrive in the limit order book via a point process correlated with the stock price, and taking into account the adverse selection risk. We apply stochastic control methods in this semi-Markov framework, and show how to reduce remarkably the complexity of the associated Hamilton-Jacobi-Bellman equation by suitable change of variables that exploits the specific symmetry of the problem. We then handle numerically the remaining part of the HJB equation, simplified into an integro-ordinary differential equation, by a bidimensional Euler scheme. Statistical procedures and numerical tests for computing the optimal limit order strategies illustrate our results. |
| Keywords: | High frequency trading, Markov renewal process, Marked Cox process, adverse selection, integro-ordinary differential equation. |
| Date: | 2013–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00867113&r=mst |
| By: | Dugast, J. |
| Abstract: | I model the speed of price adjustments to news arrival in limit order markets when investors have limited attention. Because of limited attention, investors imperfectly monitor news arrival. Consequently, in equilibrium, prices reflect news with delay. This delay shrinks when investors' attention capacity increases. The price adjustment delay also decreases when the frequency of news arrival increases. When news arrival frequency is higher, the picking-off risk increases for limit orders. The limit order book becomes thinner and there are fewer stale limit orders to execute or cancel after news arrival. Thus, it reduces the time it takes for market prices to reflect news content. |
| Keywords: | financial market, limit order market, news, limited attention, imperfect market monitoring. |
| JEL: | G14 D82 D83 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:bfr:banfra:449&r=mst |
| By: | Jose Blanchet; Xinyun Chen |
| Abstract: | We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our asymptotic analysis using stylized features observed empirically. We argue that in the asymptotic regime supported by empirical observations the mid price and bid-ask-spread can be described using only certain parameters of the book (not the whole book itself). Our limit process is characterized by reflecting behavior and state-dependent jumps. Our analysis allows to explain certain characteristics observed in practice such as: the connection between power-law decaying tails in the volumes of the order book and the returns, as well as statistical properties of the long-run spread distribution. |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1310.1103&r=mst |
| By: | Marine Carrasco (CIREQ - Centre interuniversitaire de recherche en économie quantitative - Université de Montréal); Rachidi Kotchoni (THEMA - Théorie économique, modélisation et applications - CNRS : UMR8184 - Université de Cergy Pontoise) |
| Abstract: | We design adaptive realized kernels to estimate the integrated volatility in a framework that combines a stochastic volatility model with leverage effect for the efficient price and a semiparametric microstructure noise model speci ed at the highest frequency. Some time dependence parameters of the noise model must be estimated before adaptive realized kernels can be implemented. We study their performance by simulation and illustrate their use with twelve stocks listed in the Dow Jones Industrial. As expected, we nd that adaptive realized kernels achieves the optimal trade-off between the discretization error and the microstructure noise. |
| Keywords: | Integrated Volatility, Method of Moment, Microstructure Noise, Realized Kernels |
| Date: | 2013–09–30 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00867967&r=mst |