
on Market Microstructure 
By:  Torben G. Andersen (Northwestern University, NBER, and CREATES); Martin Thyrsgaard (Aarhus University and CREATES); Viktor Todorov (Northwestern University) 
Abstract:  We develop a nonparametric test for deciding whether return volatility exhibits timevarying intraday periodicity using a long timeseries of highfrequency data. Our null hypothesis, commonly adopted in work on volatility modeling, is that volatility follows a stationary process combined with a constant timeofday periodic component. We first construct timeofday volatility estimates and studentize the highfrequency returns with these periodic components. If the intraday volatility periodicity is invariant over time, then the distribution of the studentized returns should be identical across the trading day. Consequently, the test is based on comparing the empirical characteristic function of the studentized returns across the trading day. The limit distribution of the test depends on the error in recovering volatility from discrete return data and the empirical process error associated with estimating volatility moments through their sample counterparts. Critical values are computed via easytoimplement simulation. In an empirical application to S&P 500 index returns, we find strong evidence for variation in the intraday volatility pattern driven in part by the current level of volatility. When market volatility is elevated, the period preceding the market close constitutes a significantly higher fraction of the total daily integrated volatility than is the case during low market volatility regimes. 
Keywords:  highfrequency data, periodicity, semimartingale, specification test, stochastic volatility 
JEL:  C51 C52 G12 
Date:  2018–01–12 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201805&r=all 
By:  Diego Zabaljauregui; Luciano Campi 
Abstract:  Starting from the AvellanedaStoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time interval, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes, but also on unobservable factors modelled by a hidden Markov chain. We tackle this stochastic control problem under partial information with a model that unifies and generalizes many existing ones, combining several risk metrics and constraints, and using general decreasing intensity functionals. We use stochastic filtering, control and piecewisedeterministic Markov processes theory, to reduce the dimensionality of the problem and characterize the reduced value function as the unique continuous viscosity solution of its dynamic programming equation. We then solve the analogous full information problem and compare the results numerically through a concrete example. We show that the optimal full information spreads are biased when the exact market regime is unknown, and the MM needs to adjust for `regime risk' in terms of liquidity volatility and sensitivity to regime changes. This effect becomes higher the longer the waiting time in between orders. 
Date:  2019–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1902.01157&r=all 
By:  Faisal I Qureshi 
Abstract:  With the proliferation of algorithmic highfrequency trading in financial markets, the Limit Order Book has generated increased research interest. Research is still at an early stage and there is much we do not understand about the dynamics of Limit Order Books. In this paper, we employ a machine learning approach to investigate Limit Order Book features and their potential to predict short term price movements. This is an initial broadbased investigation that results in some novel observations about LOB dynamics and identifies several promising directions for further research. Furthermore, we obtain prediction results that are significantly superior to a baseline predictor. 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1901.10534&r=all 
By:  Torben G. Andersen (Northwestern University and CREATES); Nicola Fusari (The Johns Hopkins University Carey Business School); Viktor Todorov (Northwestern University); Rasmus T. Varneskov (Northwestern University and CREATES) 
Abstract:  We develop parametric inference procedures for large panels of noisy option data in the setting where the underlying process is of purejump type, i.e., evolve only through a sequence of jumps. The panel consists of options written on the underlying asset with a (different) set of strikes and maturities available across observation times. We consider the asymptotic setting in which the crosssectional dimension of the panel increases to infinity while its time span remains fixed. The information set is further augmented with highfrequency data on the underlying asset. Given a parametric specification for the riskneutral asset return dynamics, the option prices are nonlinear functions of a timeinvariant parameter vector and a timevarying latent state vector (or factors). Furthermore, noarbitrage restrictions impose a direct link between some of the quantities that may be identified from the return and option data. These include the socalled jump activity index as well as the timevarying jump intensity. We propose penalized least squares estimation in which we minimize L_2 distance between observed and modelimplied options and further penalize for the deviation of modelimplied quantities from their modelfree counterparts measured via the highfrequency returns. We derive the joint asymptotic distribution of the parameters, factor realizations and highfrequency measures, which is mixed Gaussian. The different components of the parameter and state vector can exhibit different rates of convergence depending on the relative informativeness of the highfrequency return data and the option panel. 
Keywords:  Inference, Jump Activity, Large Data Sets, Nonlinear Factor Model, Options, Panel Data, Stable Convergence, Stochastic Jump Intensity 
JEL:  C51 C52 G12 
Date:  2018–01–10 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201804&r=all 