Chair of Quantitative Finance

# Workshop – Portfolio dynamics and limit order books

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 9:30-10:10 Title Parametric inference for diffusion processes with high-frequency data Abstract We study statistical inference for security prices modeled by diffusion processes with high-frequency observations. In particular, we focus on two problems on analysis of high-frequency data, that is, nonsynchronous observations and the presence of observation noise called market microstructure noise. We propose maximum-likelihood-type 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 maximum-likelihood-type estimator.

 Speaker Yoann Potiron Time 10:10-10:50 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 [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 is investigated using simulations, while our empirical work illustrates the expected gain in practice.

Break

 Speaker Xiaofei Lu Time 11:10-11:50 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 2-dimensional Hawkes process price model, especially to compare the full model with that restricted to pure cross-excitation and the use of 1 or 2 exponential functions for the kernel. A 12-dimensional 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 mid-price). 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 non-linear Hawkes process to model inhibiting relations. The resulting model conforms well with the real event dependences, and exhibits close high-frequency and low-frequency volatilities in signature plots.

 Speaker Simon Clinet Time 11:50-12:30 Title Estimating the Integrated Parameter of the Time-Varying Parameter Self-Exciting Process Abstract We introduce and show the existence of a continuous time-varying parameter extension model to the self-exciting 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 time-varying 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 non-naive estimator, which is constructed as the naive one when applying a first-order bias reduction to the local MLE. We derive such first-order bias formula for the self-exciting process, and provide further conditions under which the non-na\”{i}ve global estimator is asymptotically unbiased. Finally, we obtain the associated global central limit theorem.

Lunch Break

 Speaker Marcus Cordi Time 14:30-15:10 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 cross-excitation (between individuals or groups) and self-excitation. When analysing real-world data, a significant challenge is non-stationarity. A simple Poisson process with non-stationary rates may be mistaken for a Hawkes process. The Hawkes process appears to have certain (nearly) time-reversible properties.

 Speaker Yuta Koike Time 15:10-15:50 Title Statistical lead-lag effects Abstract A lead-lag 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 cross-correlogram between two time series. In high-frequency financial data there are some cases where the cross-correlograms between the intra-daily 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 lead-lag effects. In this talk we aim at developing a model having the ability to describe statistical lead-lag effects. We also propose a statistical methodology to estimate statistical characteristics of the statistical lead-lag effects between two time series from their high-frequency 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 16:10-16:50 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 16:50-17:30 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 low-dimensional, and only fit well the long-term 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 micro-structural 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 high-dimensional realistic models in a micro-structure 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.
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### Coordinates

Chair of Quantitative Finance
Laboratoire de Mathématiques et Informatique pour la Complexité et les Systèmes

CentraleSupélec
9 rue Joliot-Curie
91190 Gif-sur-Yvette
FRANCE