A shrinking horizon optimal liquidation framework with lower partial moments criteria

In this paper, a novel quasi-multiperiod model for optimal position liquidation in the presence of both temporary and permanent market impact is proposed. Two main features distinguish the proposed approach from its alternatives. First, a shrinking horizon framework is implemented to update intraday parameters by incorporating new incoming information while maintaining standard nonanticipativity constraints. The method is data-driven, numerically tractable and reactive to the market. Second, lower partial moments, a downside risk measure, is used. Unlike symmetric measures, such as variance, this captures traders’ increased risk aversion to losses. The performance of the proposed strategies is tested using historical, high-frequency New York Stock Exchange data. All proposed strategies outperform classic strategies such as a time-weighted average price strategy as well as more unrealistic strategies such as an ex-post volume-weighted average price strategy that violates nonantici- pativity on days with unfavorable market conditions; this strongly supports the use of lower partial moments as a risk measure. In addition, the papers results validate the use of a shrinking horizon framework as an adaptive, tractable alternative to dynamic programming for trading.