
on Market Microstructure 
By:  Friedrich Hubalek; Paul Kr\"uhner; Thorsten Rheinl\"ander 
Abstract:  We study a parsimonious but nontrivial model of the latent limit order book where orders get placed with a fixed displacement from a center price process, i.e.\ some process inbetween best bid and best ask, and get executed whenever this center price reaches their level. This mechanism corresponds to the fundamental solution of the stochastic heat equation with multiplicative noise for the relative order volume distribution. We classify various types of trades, and introduce the trading excursion process which is a Poisson point process. This allows to derive the Laplace transforms of the times to various trading events under the corresponding intensity measure. As a main application, we study the distribution of order avalanches, i.e.\ a series of order executions not interrupted by more than an $\varepsilon$time interval, which moreover generalizes recent results about Parisian options. 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1701.00993&r=mst 
By:  Antoine Jacquier; Hao Liu 
Abstract:  We propose a framework to study the optimal liquidation strategy in a limit order book for largetick stocks, with spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to independent Poisson processes, with parameters depending on price move directions. Our goal is to maximise the expected terminal wealth of an agent who needs to liquidate her positions within a fixed time horizon. Assuming that the agent trades (through sell limit order or/and sell market order) only when the price moves, we model her liquidation procedure as a semiMarkov decision process, and compute the semiMarkov kernel using Laplace method in the language of queueing theory. The optimal liquidation policy is then solved by dynamic programming, and illustrated numerically. 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1701.01327&r=mst 
By:  B Bouchard (CEREMADE  CEntre de REcherches en MAthématiques de la DEcision  CNRS  Centre National de la Recherche Scientifique  Université ParisDauphine, CREST  Centre de Recherche en Économie et Statistique  INSEE  École Nationale de la Statistique et de l'Administration Économique); G Loeper (FiQuant  Chaire de finance quantitative  Ecole Centrale Paris); Y Zou (CEREMADE  CEntre de REcherches en MAthématiques de la DEcision  CNRS  Centre National de la Recherche Scientifique  Université ParisDauphine, CREST  Centre de Recherche en Économie et Statistique  INSEE  École Nationale de la Statistique et de l'Administration Économique) 
Abstract:  We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of superhedging a European option. Our main result is the derivation of a quasilinear pricing equation. It holds in the sense of viscosity solutions. When it admits a smooth solution, it provides a perfect hedging strategy. 
Keywords:  Price impact.,Hedging 
Date:  2016–06–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal01133223&r=mst 
By:  Aurélien Alfonsi (CERMICS  Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique  École des Ponts ParisTech (ENPC)  UPE  Université ParisEst , MATHRISK  Mathematical Risk Handling  UPEM  Université ParisEst MarnelaVallée  École des Ponts ParisTech (ENPC)  Inria de Paris  Inria  Institut National de Recherche en Informatique et en Automatique); Pierre Blanc (CERMICS  Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique  École des Ponts ParisTech (ENPC)  UPE  Université ParisEst , MATHRISK  Mathematical Risk Handling  UPEM  Université ParisEst MarnelaVallée  École des Ponts ParisTech (ENPC)  Inria de Paris  Inria  Institut National de Recherche en Informatique et en Automatique) 
Abstract:  We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closedformula optimal strategy describes in particular how one should react to the orders of other traders. This result enables us to discuss the viability of the market. It is shown that Poissonian arrivals of orders lead to quite robust Price Manipulation Strategies in the sense of Huberman and Stanzl. Instead, a particular set of conditions on the Hawkes model balances the selfexcitation of the order flow with the resilience of the price, excludes Price Manipulation Strategies and gives some market stability. 
Date:  2016–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal00971369&r=mst 
By:  Michael Schneider; Fabrizio Lillo 
Abstract:  We extend the "Nodynamicarbitrage and market impact"framework of Jim Gatheral [Quantitative Finance, 10(7): 749759 (2010)] to the multidimensional case where trading in one asset has a crossimpact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of crossimpact that can be directly verified on data. For bounded decay kernels we find that crossimpact must be an odd and linear function of trading intensity and crossimpact from asset $i$ to asset $j$ must be equal to the one from $j$ to $i$. To test these constraints we estimate crossimpact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of crossimpact, we show that these are not arbitrageable with simple strategies because of the presence of the bidask spread. 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1612.07742&r=mst 
By:  Simon Clinet; Yoann Potiron 
Abstract:  This paper shows how to carry out efficient asymptotic variance reduction when estimating volatility in the presence of stochastic volatility and microstructure noise with the realized kernels (RK) from [BarndorffNielsen et al., 2008] and the quasimaximum likelihood estimator (QMLE) studied in [Xiu, 2010]. To obtain such a reduction, we chop the data into B blocks, compute the RK (or QMLE) on each block, and aggregate the block estimates. The ratio of asymptotic variance over the bound of asymptotic efficiency converges as B increases to the ratio in the parametric version of the problem, i.e. 1.0025 in the case of the fastest RK TukeyHanning 16 and 1 for the QMLE. The finite sample performance of both estimators is investigated in simulations, while empirical work illustrates the gain in practice. 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1701.01185&r=mst 
By:  Tim Leung; Yerkin Kitapbayev 
Abstract:  We study several optimal stopping problems that arise from trading a meanreverting price spread over a finite horizon. Modeling the spread by the OrnsteinUhlenbeck process, we analyze three different trading strategies: (i) the longshort strategy; (ii) the shortlong strategy, and (iii) the chooser strategy, i.e. the trader can enter into the spread by taking either long or short position. In each of these cases, we solve an optimal double stopping problem to determine the optimal timing for starting and subsequently closing the position. We utilize the local timespace calculus of Peskir (2005a) and derive the nonlinear integral equations of Volterratype that uniquely char acterize the boundaries associated with the optimal timing decisions in all three problems. These integral equations are used to numerically compute the optimal boundaries. 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1701.00875&r=mst 