Inventory management in customised liquidity pools

We consider “customised liquidity pools” (CLP), which are trading venues that offer over-the-counter brokerage and dealer services to selected market participants. The dealer activity, whereby two-sided liquidity is offered to a limited pool of clients, shares in common similarities with the market-making problem. The arrival flow of client orders is assumed random. The CLP offers a stream of two-way prices to its clients, which are functions of the amount traded by the client and the CLP holding. The concern is inventory risk, which increases for critically small or large numbers of held positions. The CLP controls its inventory by choosing the size and the skew of its spread, so to encourage, e.g. buy orders instead of sell orders. Furthermore, it can submit limit orders to standard exchanges, of which execution is uncertain, and market orders, which are expensive. In either case, the CLP risks information leakage, which is discouraged by a penalty for trading in standard exchanges. We numerically solve a double-obstacle impulse-control problem associated with the optimal management of the inventory. We observe that the CLP skews its spread before resorting to limit orders, and ultimately crosses the spread in the standard exchange. We learn that it is optimal to post limit orders deeper in the book when the inventory is relatively small and to progressively move towards the best price as the inventory increases. The CLP adjusts its pricing-hedging strategy according to its profit and losses (P&L) target, a feature we analyse by considering various degrees of the CLP’s risk appetite