Dynamic optimal execution models with transient market impact and downside risk

When institutional investors trade large amounts of stock in the market, the trading amount might impact the price, and this price change is called market impact (MI hereafter). In addition, their trading is always exposed to uncertain price change, and this is called timing risk. Such investors need to quantitatively evaluate the MI and timing risk, and decide the optimal execution strategy when considering the trade-off between them. Several previous studies assume temporary/permanent MI, while some recent studies discuss transient MI. On the contrary, most investors need to manage their downside risk when executing an order to meet the trading needs below a target cost. In this study, we discuss dynamic optimization models with transient MI and downside risk in order to decide the optimal execution strategy. Specifically, we propose the following three types of models based on Takenobu and Hibiki (2016) who assume temporary/permanent MI. (1) Multiperiod model with step function using Monte Carlo simulation (Step model); (2) Multiperiod model with piecewise linear (PwL) function based on the Step model; and (3) One-period iterative model with static execution strategy (Iterative model). We solve the optimal execution problems using these models, and conduct a sensitivity analysis to examine the benefits of the models. In addition, we compare the three models, and evaluate their characteristics and differences. We estimate the MI function and other parameters using market data, and derive the optimal execution strategies for practical use.