Order Oversizing in Markets with Pro-Rata Matching Algorithms

Abstract

Financial exchanges use various algorithms to match limit orders resting in the order book with incoming market orders. The most common type of matching algorithm is “time priority:” when a market order arrives, resting limit orders are filled in the order they were entered into the order book. However, some exchanges and products use pro-rata matching. The algorithm allocates the incoming order size to the orders in the book proportionally to their relative sizes. This is most often used for products like short interest rate futures contracts. In the markets where pro-rata matching is used, market orders are typically small and scarce. The participants posting limit orders want to get as close as possible to their desired fill. Traders increase their order size in order to compete with the other participants and get as big of a share of the small market order as possible. There is however a risk of overfill if a large market order were to enter the book. The question this paper is trying to answer is how does the effect of oversizing to get an optimal fill interact with the overfill risk, and how does this interaction prevent oversizing from growing unbounded.