Optimal Execution When the Required Trading Volume Is Uncertain

Summary

This document extends the Almgren–Chriss optimal execution setting, which assumes a fixed quantity to liquidate, to cases where the required trading volume is uncertain and becomes clearer as a delivery deadline approaches. Power markets are offered as an example of this type of problem. The trader must adapt execution as the estimate changes over time.

The proposed model adds a risk term for uncertainty in the quantity to be traded. It argues that a risk-averse trader may benefit from delaying some trades, while still balancing price risk against the risk of an inaccurate volume target. The resulting static strategies are presented as a way to avoid the computational burden of dynamic programming while retaining competitive performance. The excerpt provides no numerical comparisons or conditions under which the approach performs best, so its performance claim cannot be assessed from the summary alone.

Key ideas

• The model adapts optimal execution to a target quantity that remains uncertain until near delivery.
• A trader faces both price risk and the risk of misestimating the final volume.
• The proposed strategy balances early and late trading, with risk aversion favoring some delay.
• Static strategies with a volume risk term are intended to avoid dynamic programming complexity.

Tags

# Optimal Trade Execution with Uncertain Volume Target


# Optimal Trade Execution with Uncertain Volume Target









In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss (2001) define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as in the power market, in which the volume to be traded can only be estimated and becomes more accurate when approaching a specified delivery time. During the course of execution, a trader should then constantly adapt their trading strategy to meet their fluctuating volume target. In this paper, we develop a model that accounts for volume uncertainty and we show that a risk-averse trader has benefit in delaying their trades. More precisely, we argue that the optimal strategy is a trade-off between early and late trades in order to balance risk associated with both price and volume. By incorporating a risk term related to the volume to trade, the static optimal strategies suggested by our model avoid the explosion in the algorithmic complexity usually associated with dynamic programming solutions, all the while yielding competitive performance.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.