Workshop – Portfolio dynamics and limit order books
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Date/Time
Date(s)  12/12/2016
9:30 am  6:30 pm
Location
Ecole CentraleSupélec
Categories
Organizers:
– Simon Clinet (University of Tokyo)
– Kevin Primicerio (Ecole CentraleSupélec)
This workshop is supported by:
– University of Tokyo
– CREST Japan Science and Technology Agency
– CentraleSupélec
Speakers:
Marcus Cordi (CentraleSupélec)
Simon Clinet (University of Tokyo)
Come Huré (Université Paris Denis Diderot and CentraleSupélec)
Yuta Koike (Tokyo Metropolitan University)
Xiaofei Lu (CentraleSupélec)
Teppei Ogihara (ISM Tokyo)
Yoann Potiron (Keio University)
Kevin Primicerio (CentraleSupélec)
Speaker  Teppei Ogihara 
Time  9:3010:10 
Title  Parametric inference for diffusion processes with highfrequency data 
Abstract  We study statistical inference for security prices modeled by diffusion processes with highfrequency observations. In particular, we focus on two problems on analysis of highfrequency data, that is, nonsynchronous observations and the presence of observation noise called market microstructure noise. We propose maximumlikelihoodtype estimation for parametric diffusion processes with discrete and nonsynchronous observations contaminated by market microstructure noise, and prove that our estimator has the best asymptotic variance in any estimators when diffusion processes are Brownian motions. We conjecture our estimator is also the best in general cases. We also consider nonparametric estimation based on the maximumlikelihoodtype estimator. 
Speaker  Yoann Potiron 
Time  10:1010:50 
Title  Efficient asymptotic variance reduction when estimating volatility in high frequency data 
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 is investigated using simulations, while our empirical work illustrates the expected gain in practice. 
Break
Speaker  Xiaofei Lu 
Time  11:1011:50 
Title  Limit order book modelling with high dimensional Hawkes processes 
Abstract  The limit order book (LOB) in electronic markets provides much more abundant information than just the price series. The classical approach is to model the order flows by point processes. We first show empirical evidences of structural exciting relations between different events, raising the interest and necessity of using Hawkes process for order book modelling. Then, we review the 2dimensional Hawkes process price model, especially to compare the full model with that restricted to pure crossexcitation and the use of 1 or 2 exponential functions for the kernel. A 12dimensional Hawkes process order book model is constructed to model events on bid and on ask (limit orders, market orders and cancellations that change and do not change the midprice). Exponential kernels are used in all of our models in order to benefit from the O(n) complexity (O(n^2 ) in general) for the likelihood function computation. We further propose a heuristic solution with nonlinear Hawkes process to model inhibiting relations. The resulting model conforms well with the real event dependences, and exhibits close highfrequency and lowfrequency volatilities in signature plots. 
Speaker  Simon Clinet 
Time  11:5012:30 
Title  Estimating the Integrated Parameter of the TimeVarying Parameter SelfExciting Process 
Abstract  We introduce and show the existence of a continuous timevarying parameter extension model to the selfexciting point process introduced in [Hawkes1971] . The kernel shape is assumed to be exponentially decreasing. The quantity of interest is defined as the integrated parameter over time $T^{1} \int_0^T \theta_t^* dt$, where $\theta_t^*$ is the timevarying parameter. To estimate it naively, we chop the data into several blocks, compute the maximum likelihood estimator (MLE) on each block, and take the average of the local estimates. Correspondingly, we give conditions on the parameter process and the block length under which we can establish the local central limit theorem, and the boundedness of moments of order $2\kappa$ of the local estimators, where $\kappa > 1$. Under those assumptions, the global estimator asymptotic bias explodes asymptotically. As a consequence, we provide a nonnaive estimator, which is constructed as the naive one when applying a firstorder bias reduction to the local MLE. We derive such firstorder bias formula for the selfexciting process, and provide further conditions under which the nonna\”{i}ve global estimator is asymptotically unbiased. Finally, we obtain the associated global central limit theorem. 
Lunch Break
Speaker  Marcus Cordi 
Time  14:3015:10 
Title  Determination of Investor Interaction Networks 
Abstract  In the marketplace investors interact with each other in different ways. A common approach is to assume homogeneity and utilise static methods. A promising way of modelling these interactions, which allows for heterogeneity (in the form of modelling each agent individually or by identifying various groups) and a dynamic behaviour, is to use Hawkes processes. These processes are essentially modified Poisson processes with kernels which may model crossexcitation (between individuals or groups) and selfexcitation. When analysing realworld data, a significant challenge is nonstationarity. A simple Poisson process with nonstationary rates may be mistaken for a Hawkes process. The Hawkes process appears to have certain (nearly) timereversible properties. 
Speaker  Yuta Koike 
Time  15:1015:50 
Title  Statistical leadlag effects 
Abstract  A leadlag effect is a relationship between two time series which describes a situation where one is correlated to anther with a time lag. One can visualize such a phenomenon by depicting the crosscorrelogram between two time series. In highfrequency financial data there are some cases where the crosscorrelograms between the intradaily returns of two assets fluctuate day by day, while they exhibit a regular pattern once they are averaged across days. We call such phenomenons statistical leadlag effects. In this talk we aim at developing a model having the ability to describe statistical leadlag effects. We also propose a statistical methodology to estimate statistical characteristics of the statistical leadlag effects between two time series from their highfrequency observation data. Finally, we report several numerical experiments to demonstrate how the proposed model and methodology work in practice. This is a joint work with Prof. Nakahiro Yoshida (University of Tokyo). 
Break
Speaker  Kevin Primicerio 
Time  16:1016:50 
Title  Wisdom of the Institutional Crowd 
Abstract  The portfolio structure of institutional investors is shown to account, on average, optimally for transaction costs and liquidity constraints. This implies that at a population level, financial institutions unknowingly display collective rationality, or Wisdom of the Crowd. Wisdom of the crowds is shown to hold in institutional investments. We find that the population of institutional investors collectively behaves as a rational portfolio optimizer, with very large individual fluctuations. Accounting for the constraints faced by large investment funds makes it possible to understand why their average portfolio markedly differs from that of smaller funds. 
Speaker  Côme Huré 
Time  16:5017:30 
Title  Optimal Placement of Orders in Market Making Strategies 
Abstract  We propose a framework for studying optimal market making policies in a FIFO (first in first out) limit order book (LOB). We consider a market maker who, based on the LOB, choose to buy and sell stocks on continuous basis at quoted prices; and identify the best strategies that maximize a utility function defined by the market maker as her terminal wealth plus a penalization of her inventory at a terminal time.
Many works have already been done on this subject: given different classes of models for the LOB, value functions has been characterized and efficient ways to compute optimal market making strategies have been highlighted. However one might notice that all the considered models are lowdimensional, and only fit well the longterm behaviors of the LOB. Typically, in most of the recent works,the authors modeled the price or the spread as diffusions, some introduced an execution probability to model the execution of orders in the order book. Then, the author derive characterizations for the value function.
In this paper, we consider microstructural models for the LOB. This class of models has been developed recently in the literature. The limit orders, market orders, and cancel orders arrivals in the LOB are modeled as Poisson processes with intensities that depend on the state of the LOB. These are highdimensional realistic models in a microstructure point of view.
We use the theory of Markov Decision Processes to characterize the value function associated to the market making problem as solutions of Bellman equations. Finally, we use Markovian quantization methods to compute efficiently the optimal strategies.
