  Financial exchanges provide incentives for limit order book (LOB) liquidity
provision to certain market participants, termed designated market makers or
designated sponsors. While quoting requirements typically enforce the activity
of these participants for a certain portion of the day, we argue that liquidity
demand throughout the trading day is far from uniformly distributed, and thus
this liquidity provision may not be calibrated to the demand. We propose that
quoting obligations also include requirements about the speed of liquidity
replenishment, and we recommend use of the Threshold Exceedance Duration (TED)
for this purpose. We present a comprehensive regression modelling approach
using GLM and GAMLSS models to relate the TED to the state of the LOB and
identify the regression structures that are best suited to modelling the TED.
Such an approach can be used by exchanges to set target levels of liquidity
replenishment for designated market makers.
