Algorithmic market making in dealer markets with hedging and market impact

In dealer markets, dealers provide prices at which they agree to buy and sell the assets and securities they have in their scope. With ever increasing trading volume, this quoting task has to be done algorithmically in most markets such as foreign exchange (FX) markets or corporate bond markets. Over the last 10 years, many mathematical models have been designed that can be the basis of quoting algorithms in dealer markets. Nevertheless, in most (if not all) models, the dealer is a pure internalizer, setting quotes and waiting for clients. However, on many dealer markets, dealers also have access to an interdealer market or even public trading venues where they can hedge part of their inventory. In this paper, we propose a model taking this possibility into account therefore allowing dealers to externalize part of their risk. The model displays an important feature well known to practitioners that within a certain inventory range, the dealer internalizes the flow by appropriately adjusting the quotes and starts externalizing outside of that range. The larger the franchise, the wider is the inventory range suitable for pure internalization. The model is illustrated numerically with realistic parameters for USDCNH spot market.