This paper examines the relationship between liquidity fragmentation and price jumps. Unexpected changes in intraday liquidity fragmentation predict jumps and jump direction. A shock to ask (bid) side liquidity fragmentation increases the probability of positive (negative) jumps by 36%....

We examine the role of high-frequency traders (HFTs) in price discovery and price efficiency. Overall HFTs facilitate price efficiency by trading in the direction of permanent price changes and in the opposite direction of transitory pricing errors, both on average and on the highest volatility...

We examine empirically the role of high-frequency traders (HFTs) in price discovery and price efficiency. Based on our methodology, we find overall that HFTs facilitate price efficiency by trading in the direction of permanent price changes and in the opposite direction of transitory pricing...

We analyze the contribution to price discovery of market and limit orders by high frequency traders (HFTs) and non-HFTs. While market orders have a larger individual price impact, limit orders are far more numerous. This results in price discovery occurring predominantly through limit orders....