We document trade price clustering in the futures markets. We find clustering at prices of x.00 and x.50 for S&P 500 futures contracts. While trade price clustering is evident throughout time to maturity of these contracts, there is a dramatic change when the S&P 500 futures contract is...

We study the levels of lit and dark fragmentation in IPOs. Using a sample of 451 IPOs, we find that measures of dark and lit fragmentation are higher in underpriced issues. We further test the claim that IPO price uncertainty is not fully resolved at the offering and that this ex-post...