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We study how to unwind stochastic order flow with minimal transaction costs.Stochastic order flow arises, e.g., in the central risk book (CRB), acentralized trading desk that aggregates order flows within a financialinstitution. The desk can warehouse in-flow orders, ideally netting themagainst subsequent opposite orders (internalization), or route them to themarket (externalization) and incur costs related to price impact and bid-askspread. We model and solve this problem for a general class of in-flowprocesses, enabling us to study in detail how in-flow characteristics affectoptimal strategy and core trading metrics. Our model allows for an analyticsolution in semi-closed form and is readily implementable numerically. Comparedwith a standard execution problem where the order size is known upfront, theunwind 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, wepresent extensive simulations for different use cases and regimes, andintroduce new metrics of practical interest.

Unwinding Stochastic Order Flow: When to Warehouse Trades