Title: Optimal make-take fees for market making regulation,
Abstract: We consider an exchange who wishes to set suitable make-take fees to attract
liquidity on its platform. Using a principal-agent approach, we are able to
describe in quasi-explicit form the optimal contract to propose to a market
maker. This contract depends essentially on the market maker inventory
trajectory and on the volatility of the asset. We also provide the optimal
quotes that should be displayed by the market maker. The simplicity of our
formulas allows us to analyze in details the effects of optimal contracting
with an exchange, compared to a situation without contract. We show in
particular that it leads to higher quality liquidity and lower trading costs
for investors.