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EdisonCruise
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Joined: September 15th, 2012, 4:22 am

How to implement this limit order fill rate model in practical trading?

December 15th, 2022, 12:21 pm

In paper Optimal make-take fees for market making regulation, Euch, Mastrolia, Rosenbaum, Touzi, the fill rate of limit order (Eq.2 of the paper) is \( \lambda(x)=Aexp(-k(x+c)/ \sigma) \), where k indicates the impact of market order, \( \sigma\) is volatility, c is taker fee and x is the maker’s quoted price (relative to mid price). This model and the paper’s result show that x <0 is possible, meaning that market maker can post bid(ask) order at price larger(smaller) than mid price. This model seems not true, if the bid-ask spread is regularly equal to one tick.

Usually for those exchanges with make-take fees system, if a post-only bid order is to place at price larger than best ask, it will be canceled immediately; if it is a non-post-only bid order, it will be executed at least partially and immediately, and as a result, taker fee is charged. Both cases violate the fill rate model of this paper. So I wonder how to place limit order based on this fill rate model.