Trading Foreign Exchange Triplets
We develop the optimal trading strategy for a Foreign Exchange
(FX) broker who trades a triplet of currency pairs, and requires to unwind all the pairs within a given time schedule. The broker accounts for model ambiguity in the FX rates to make her optimal strategy robust to misspecifications. She trades with her pool of clients and also trades in a major FX exchange. Specifically, the broker streams currency pair quotes to personal clients who trade directly with her, and simultaneously the broker is executing trades in the FX exchange to ensure liquidation of her positions by the terminal date. Under certain assumptions we provide a closed-form solution for the broker's optimal trading strategy. Simulations of the strategy when the pairs have varying liquidity levels are presented and verification proofs are provided.