Dealing with multi-currency inventory risk in FX cash markets

Abstract: In FX cash markets, market makers provide liquidity to clients for a wide variety of currency pairs. Because of flow uncertainty and market volatility, they face inventory risk. To mitigate this risk, they typically skew their prices to attract or divert the flow and trade with their peers on the dealer-to-dealer segment of the market for hedging purposes. This paper offers a mathematical framework to FX dealers willing to maximize their expected profit while controlling their inventory risk. Approximation techniques are proposed which make the framework scalable to any number of currency pairs.