Topics in High-Frequency Optimal Execution and Microstructure of Product Repricings

Abstract

This dissertation focuses on two main topics, one in high-frequency finance and an-other in microeconomics. The first topic is that of optimal execution of large orders by high-frequency traders. We first use a novel approach to approximating the solution of the stochastic optimization problem using deep neural networks (DNNs). This allows us to avoid making assumptions about financial data and directly use it in training. Since DNNs commonly face critiques for being “black boxes”, we also provide an explainability framework under which traders and regulators can understand the underlying risks of the model, making the solution more transparent. Then, we perform statistical tests arguing for the presence of a Brownian compo- nent in the inventories and wealth processes of individual traders within the optimal execution framework. We show that for both regularly spaced time intervals, as well for asynchronous data (i.e., the trading clock), these processes should be modelled including a diffusion component. We propose a new way of setting up the optimal execution problem, and solve it using Pontryagin’s maximum principle. Moreover, we compare Monte Carlo simulations of this new dynamic problem to the behavior of a real trader, identifying very similar behavior. Finally, we shift gears towards the microeconomic problem of product repricings. We examine the implications from state-dependent pricing models on the distribution of the number of simultaneously repricing firms. We use online scrapped data to study the effect of product complementarity on price adjustments, estimating in two differ- ent ways the parameters of the Generalized Poisson distribution which describes price adjustments. Furthermore, we study the graph networks of product repricings and show the existence of cliques and heterogeneity (in the form of influential products) in the real data, thus departing from the original assumption that price adjustments are homogeneous with respect to different products and firms.