Unwinding Stochastic Order Flow: When to Warehouse Trades

48 Pages Posted: 2 Nov 2023

See all articles by Marcel Nutz

Marcel Nutz

Columbia University

Kevin Webster

Columbia University

Long Zhao

Columbia University - Departments of Statistics and Mathematics

Date Written: October 22, 2023

Abstract

We study how to unwind stochastic order flow with minimal transaction costs. Stochastic order flow arises, e.g., in the central risk book (CRB), a centralized trading desk that aggregates order flows within a financial institution. The desk can warehouse in-flow orders, ideally netting them against subsequent opposite orders (internalization), or route them to the market (externalization) and incur costs related to price impact and bid-ask spread. We model and solve this problem for a general class of in-flow processes, enabling us to study in detail how in-flow characteristics affect optimal strategy and core trading metrics. Our model allows for an analytic solution in semi-closed form and is readily implementable numerically. Compared with a standard execution problem where the order size is known upfront, the unwind strategy exhibits an additive adjustment for projected future in flows. Its sign depends on the autocorrelation of orders; only truth-telling (martingale) flow is unwound myopically. In addition to analytic results, we present extensive simulations for different use cases and regimes, and introduce new metrics of practical interest.

Keywords: Internalization, Optimal Execution, Price Impact, Central Risk Book, Market Making

JEL Classification: G24, C6

Suggested Citation

Nutz, Marcel and Webster, Kevin and Zhao, Long, Unwinding Stochastic Order Flow: When to Warehouse Trades (October 22, 2023). Available at SSRN: https://ssrn.com/abstract=4609588 or http://dx.doi.org/10.2139/ssrn.4609588

Marcel Nutz (Contact Author)

Columbia University ( email )

Kevin Webster

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Long Zhao

Columbia University - Departments of Statistics and Mathematics ( email )

1255 Amsterdam Avenue
New York, NY 10027
United States

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