Principal Trading Arrangements: Optimality under Temporary and Permanent Price Impact

Abstract

We study the optimal execution problem in a principal-agent setting. A client contracts to purchase a large position from a dealer at a future point in time. In the interim, the dealer acquires the position from the market, choosing how to split the parent order into smaller child orders. Price impact may have a temporary and a permanent component. There is hidden action in that the client cannot directly dictate the dealer’s trades. Rather, she chooses a contract with the goal of minimizing her expected payment, taking as given how the dealer’s trading will depend on the contract. We characterize explicitly the optimal contract: it is symmetric, and numerical experimentation suggests it is U-shaped.