Trading foreign exchange triplets

We develop the optimal trading strategy for a foreign exchange (FX) broker who must liquidate a large position in an illiquid currency pair. To maximize revenues, the broker considers
trading in a currency triplet which consists of the illiquid pair and two other liquid currency
pairs. The liquid pairs in the triplet are chosen so that one of the pairs is redundant. The
broker is risk-neutral and accounts for model ambiguity in the FX rates to make her strategy
robust to model misspecification. When the broker is ambiguity neutral (averse) the trading
strategy in each pair is independent (dependent) of the inventory in the other two pairs in the
triplet. We employ simulations to illustrate how the robust strategies perform. For a range
of ambiguity aversion parameters, we find the mean Profit and Loss (P&L) of the strategy
increases and the standard deviation of the P&L decreases as ambiguity aversion increases.