We develop a new likelihood-based approach to sign trades in the absence of quotes. It is equally efficient as existing MCMC methods, but more than 10 times faster. It can deal with the occurrence of multiple trades at the same time, and noisily observed trade times. We apply this method to a...

Speeding up the exchange does not necessarily improve liquidity. The price quotes of high-frequency market makers are more likely to meet speculative high-frequency "bandits", thus less likely to meet liquidity traders. The bid-ask spread is raised in response. The recursive dynamic model...