Optimal Execution with Quadratic Variation Inventories

26 Pages Posted: 4 May 2021

See all articles by Rene Carmona

Rene Carmona

Princeton University - Bendheim Center for Finance

Laura Leal

Princeton University

Date Written: April 29, 2021


The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intra-day data from the Toronto Stock Exchange to provide empirical evidence of this claim. We work with regularly spaced time intervals, as well as with asynchronously observed data. The tests reveal with high significance the presence of a non-zero Brownian motion component. The second half of the paper is concerned with the analysis of trader behaviors throughout the day. We extend the theoretical analysis of an existing optimal execution model to accommodate the presence of It\^o inventory processes, and we compare empirically the optimal behavior of traders in such fitted models, to their actual behavior as inferred from the data.

Keywords: Quantitative Finance, High-Frequency Econometrics, Quadratic Variation, Brownian Motion

JEL Classification: C22, C44, G12

Suggested Citation

Carmona, Rene and Leal, Laura, Optimal Execution with Quadratic Variation Inventories (April 29, 2021). Available at SSRN: https://ssrn.com/abstract=3836898 or http://dx.doi.org/10.2139/ssrn.3836898

Rene Carmona (Contact Author)

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States

Laura Leal

Princeton University ( email )

United States

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