FX is a highly fragmented delocalized marketplace combining significant OTC and open market segments. Dealers make money by providing liquidity to clients while charging spread but face flow uncertainty and thus price risk. They can skew prices to attract directional flow but ultimately have to wait for clients to mitigate risk (internalization), or they can trade with other dealers in the open market on demand to hedge their position and reduce their inventory (externalization). Better control associated with externalization comes with transaction cost and market impact. The internalization vs. externalization dilemma has been a topic of recent active discussion within the FX community. We offer an optimal control framework tackling both pricing and hedging thus constituting an important and natural encounter between two problems that have attracted a lot of academic and practitioner’s interest in the last two decades: optimal market making and optimal execution. The model allows one to set optimal pricing ladder for different tiers, or types of client flow, and determine optimal hedging rate in external liquidity pools as functions of the inventory, risk aversion and market-driven parameters. In particular, we have proven the existence of a pure flow internalization area, or equivalently, an inventory threshold below which it is optimal for the dealer not to externalize. We further generalize the model to a multi-currency portfolio and provide an optimal solution taking into account correlations and crosses. Approximation techniques are proposed which make the framework scalable to any realistic number of currency pairs.
The talk is based on joint work with Philippe Bergault and Olivier Guéant. More details can be found in the following references:
1. Algorithmic market making in dealer markets with hedging and market impact, https://doi.org/10.1111/mafi.12367
2. Market-making by a foreign exchange dealer, https://www.risk.net/7952481
3. Dealing with multi-currency inventory risk in FX cash markets, https://arxiv.org/abs/2207.04100