Optimal control of execution costs

Abstract

We derive dynamic optimal trading strategies that minimize the expected cost of trading a large block of equity over a fixed time horizon. Specifically, given a fixed block SM of shares to be executed within a fixed finite number of periods ¹, and given a price-impact function that yields the execution price of an individual trade as a function of the shares traded and market conditions, we obtain the optimal sequence of trades as a function of market conditions -closed-form expressions in some casesthat minimizes the expected cost of executing SM within ¹ periods. Our analysis is extended to the portfolio case in which price impact across stocks can have an important effect on the total cost of trading a portfolio.1998 Elsevier Science B.V. All rights reserved. JEL classification: G23

The Impact of Iceberg Orders in Limit Order Books

“…Likewise, a market order submitter who trades against a detected iceberg order solves a special dynamic order submission problem since the iceberg order temporarily makes the order book perfectly resilient after each executed peak. Under what assumptions can we rationalize these types of strategies in existing dynamic models of optimal trading such as Bertsimas and Lo (1998) DPW. We use the following cut-offs for peak size categories: 1-1,500 shares ⇒ 1K; 1,501-2,500 ⇒ 2K; 2,501-3,500 ⇒ 3K; 3,501-7,500 ⇒ 5K; 7,501+ ⇒ 10K; and total size categories: 1-7,500 shares ⇒ 5K; 7,501-12,500 ⇒ 10K; 12,501-17,500 ⇒ 15K; 17,501-35,000 ⇒ 20K; 35,001+ ⇒ 50K.…”

Mini-Flash Crashes, Model Risk, and Optimal Execution

“…Much of the previous work in this area assumes that agents have complete and correct knowledge of all model parameters ( [34], [15], [16], [18], [85], [64], [86], [32]). Others consider the possibility that their agents' models have the correct form; however, the agents must gradually learn the values of certain unobserved features ( [17], [31], [43], [54], [62], [48]).…”

How efficiency shapes market impact

“…Viswanathan and Wang (2002), Glosten (2003), and Back and Baruch (2007) derive and compare the equilibrium transaction prices of orders submitted to markets with uniform vs. discriminatory pricing. Depending on the setup of the model, these prices can be different so that investors will prefer one pricing structure to the other and can potentially be "cream-skimmed" by a competing exchange 11 . The fair pricing condition we introduce here forces the average transaction price of a metaorder (which transacts at discriminatory prices) to be equal to the price that would be set under uniform pricing.…”