arXiv subjects

Simon Clinet

Publications and source records attributed to Simon Clinet.

9 recordsLinked to original sources

arXiv2021

Optimal trading: a model predictive control approach

We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including a price mean-reversion signal into the optimization program, in a trading environment where market impact is linear and stage costs are quadratic, we obtain an optimal trading curve that reacts opportunistically to price changes while retaining its ability to satisfy smooth or hard completion constraints. The optimal allocation is affine in the spot price and in the number of outstanding shares at any time, and it can be fully derived iteratively. It is also aggressive in the money, meaning that it accelerates whenever the price is favorable, with an intensity that can be calibrated by the practitioner. Since the LQR may yield locally negative participation rates (i.e round trip trades) which are often undesirable, we show that the aforementioned optimization problem can be improved and solved under positivity constraints following a Model Predictive Control (MPC) approach. In particular, it is smoother and more consistent with the completion constraint than putting a hard floor on the participation rate. We finally examine how the LQR can be simplified in the continuous trading context, which allows us to derive a closed formula for the trading curve under further assumptions, and we document a two-step strategy for the case where trades can also occur in an additional dark pool.

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arXiv2020

Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes

We develop a quasi-likelihood analysis procedure for a general class of multivariate marked point processes. As a by-product of the general method, we establish under stability and ergodicity conditions the local asymptotic normality of the quasi-log likelihood, along with the convergence of moments of quasi-likelihood and quasi-Bayesian estimators. To illustrate the general approach, we then turn our attention to a class of multivariate marked Hawkes processes with generalized exponential kernels, comprising among others the so-called Erlang kernels. We provide explicit conditions on the kernel functions and the mark dynamics under which a certain transformation of the original process is Markovian and $V$-geometrically ergodic. We finally prove that the latter result, which is of interest in its own right, constitutes the key ingredient to show that the generalized exponential Hawkes process falls under the scope of application of the quasi-likelihood analysis.

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arXiv2019

Cointegration in high frequency data

In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless It\^{o}-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high frequency. We develop a regression based estimation of the cointegrated relations method and show the related consistency and central limit theory when there is cointegration within that framework. We also provide a Dickey-Fuller type residual based test for the null of no cointegration against the alternative of cointegration, along with its limit theory. Under no cointegration, the asymptotic limit is the same as that of the original Dickey-Fuller residual based test, so that critical values can be easily tabulated in the same way. Finite sample indicates adequate size and good power properties in a variety of realistic configurations, outperforming original Dickey-Fuller and Phillips-Perron type residual based tests, whose sizes are distorted by non ergodic time-varying variance and power is altered by price jumps. Two empirical examples consolidate the Monte-Carlo evidence that the adapted tests can be rejected while the original tests are not, and vice versa.

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arXiv2019

Asymptotic Distribution of the Score Test for Detecting Marks in Hawkes Processes

The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against local alternatives is also established as non-central chi-squared. These asymptotic results are derived using existing asymptotic results for likelihood estimates of the unmarked Hawkes process model together with mild additional conditions on the moments and ergodicity of the marks process and an additional uniform boundedness assumption, shown to be true for the exponential decay Hawkes process.

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arXiv2017

Estimation for high-frequency data under parametric market microstructure noise

We develop a general class of noise-robust estimators based on the existing estimators in the non-noisy high-frequency data literature. The microstructure noise is a parametric function of the limit order book. The noise-robust estimators are constructed as plug-in versions of their counterparts, where we replace the efficient price, which is non-observable, by an estimator based on the raw price and limit order book data. We show that the technology can be applied to five leading examples where, depending on the problem, price possibly includes infinite jump activity and sampling times encompass asynchronicity and endogeneity.

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arXiv2017

Testing if the market microstructure noise is fully explained by the informational content of some variables from the limit order book

In this paper, we build tests for the presence of residual noise in a model where the market microstructure noise is a known parametric function of some variables from the limit order book. The tests compare two distinct quasi-maximum likelihood estimators of volatility, where the related model includes a residual noise in the market microstructure noise or not. The limit theory is investigated in a general nonparametric framework. In the presence of residual noise, we examine the central limit theory of the related quasi-maximum likelihood estimation approach.

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arXiv2017

Efficient asymptotic variance reduction when estimating volatility in high frequency data

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 impact of stochastic sampling times and jump in the price process is examined carefully. The finite sample performance of both estimators is investigated in simulations, while empirical work illustrates the gain in practice.

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arXiv2016

Statistical inference for the doubly stochastic self-exciting process

We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter $T^{-1}\int_0^T\theta_t^*dt$, where $\theta_t^*$ is the time-varying parameter, and we consider the high-frequency asymptotics. To estimate it na\"ively, we chop the data into several blocks, compute the maximum likelihood estimator (MLE) on each block, and take the average of the local estimates. The asymptotic bias explodes asymptotically, thus we provide a non-na\"ive estimator which is constructed as the na\"ive one when applying a first-order bias reduction to the local MLE. We show the associated central limit theorem. Monte Carlo simulations show the importance of the bias correction and that the method performs well in finite sample, whereas the empirical study discusses the implementation in practice and documents the stochastic behavior of the parameters.

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arXiv2015

Statistical Inference for Ergodic Point Processes and Application to Limit Order Book

We construct a general procedure for the Quasi Likelihood Analysis applied to a multivariate point process on the real half line in an ergodic framework. More precisely, we assume that the stochastic intensity of the underlying model belongs to a family of processes indexed by a finite dimensional parameter. When a particular family of laws of large numbers applies to those processes, we establish the consistency, the asymptotic normality and the convergence of moments of both the Quasi Maximum Likelihood estimator and the Quasi Bayesian estimator. In addition, we illustrate our main results by showing how they can be applied to various Limit Order Book models existing in the literature. In particular, we address the fundamental cases of Markovian models and exponential Hawkes process-based models.

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