Optimal Contracts for Delegated Order Execution

ABSTRACT We determine the optimal affine contract for a client who delegates their order execution to a dealer. Existence and uniqueness are established for general linear price impact dynamics of the dealer's trades. Explicit solutions are available for the model of Obizhaeva and Wang, for example, and a simple gradient descent algorithm is applicable in general. The optimal contract allows the client to almost achieve the first‐best performance without any agency conflicts for many reasonable parameter values. Common trading arrangements arise as limiting cases. In particular, optimal contracts for many reasonable model parameters resemble the “fixing contract” common in FX markets, in that they only incorporate market prices briefly before the conclusion of the trade. Price manipulation by the dealer is avoided by only putting a sufficiently small weight on these prices, and complementing this part of the contract with a sufficiently large fixed fee.