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on Market Microstructure |
| By: | Friedrich Hubalek; Paul Kr\"uhner; Thorsten Rheinl\"ander |
| Abstract: | We study a parsimonious but non-trivial model of the latent limit order book where orders get placed with a fixed displacement from a center price process, i.e.\ some process in-between 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 large-tick 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 semi-Markov decision process, and compute the semi-Markov 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 Paris-Dauphine, 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 Paris-Dauphine, 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 re-balancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear 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:hal-01133223&r=mst |
| By: | Aurélien Alfonsi (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - École des Ponts ParisTech (ENPC) - UPE - Université Paris-Est , MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - 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 Paris-Est , MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - 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 closed-formula 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 self-excitation 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:hal-00971369&r=mst |
| By: | Michael Schneider; Fabrizio Lillo |
| Abstract: | We extend the "No-dynamic-arbitrage and market impact"-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multi-dimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset $i$ to asset $j$ must be equal to the one from $j$ to $i$. To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask 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 [Barndorff-Nielsen et al., 2008] and the quasi-maximum 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 Tukey-Hanning 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 mean-reverting price spread over a finite horizon. Modeling the spread by the Ornstein-Uhlenbeck process, we analyze three different trading strategies: (i) the long-short strategy; (ii) the short-long 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 time-space calculus of Peskir (2005a) and derive the nonlinear integral equations of Volterra-type 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 |