Optimal Execution Comparison Across Risks and Dynamics, with Solutions for Displaced Diffusions
21 Pages Posted: 11 Apr 2013 Last revised: 10 May 2014
Date Written: May 9, 2014
Abstract
We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies in the adapted class under various risk criteria, namely value-at-risk, expected shortfall and a new criterion called "squared asset expectation" (SAE), related to a version of the cost variance measure, are derived and compared. It is well known that displaced diffusions (DD) exhibit dynamics which are in-between arithmetic Brownian motions (ABM) and geometric Brownian motions (GBM) depending of the choice of the shift parameter. Furthermore, DD allows for changes in the support of the mid asset price distribution, allowing one to include a minimum permitted value for the mid price, either positive or negative. We study the dependence of the optimal solution on the choice of the risk aversion criterion. Optimal solutions across criteria and asset dynamics are comparable although differences are not negligible for high levels of risk aversion and low market impact assets. This is illustrated with numerical examples.
Keywords: Optimal trade execution, Algorithmic trading, Displaced Diffusion, HJB equation, calculus of variations, risk measures, Value at Risk, Expected Shortfall, Squared-Asset Expectation, Market Impact
JEL Classification: C51, G12, G13
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Execution Strategies in Limit Order Books with General Shape Functions
By Aurélien Alfonsi, Antje Fruth, ...
-
By Olaf Korn and Alexander Kempf
-
Quasi-Arbitrage and Price Manipulation
By Gur Huberman and Werner Stanzl
-
Fluctuations and Response in Financial Markets: The Subtle Nature of 'Random' Price Changes
By Jean-philippe Bouchaud, Yuval Gefen, ...
-
By Gur Huberman and Werner Stanzl
-
How Markets Slowly Digest Changes in Supply and Demand
By Jean-philippe Bouchaud, J. Doyne Farmer, ...
-
No-Dynamic-Arbitrage and Market Impact
By Jim Gatheral