> We argue that the high-frequency trading arms race is a symptom of a basic flaw in the design of modern financial exchanges: continuous-time trading. That is, under the continuous limit order book market design that is currently predominant, it is possible to buy or sell stocks or other exchange-traded financial instruments at any instant during the trading day. We propose a simple alternative: discrete-time trading. More precisely, we propose a market design in which the trading day is divided into extremely frequent but discrete time intervals; to fix ideas, say, 100 milliseconds. All trade requests received during the same interval are treated as having arrived at the same (discrete) time. Then, at the end of each interval, all outstanding orders are processed in batch, using a uniform-price auction, as opposed to the serial processing that occurs in the continuous market. We call this market design frequent batch auctions.

This raises a question in my mind. 100 milliseconds seems really short, but I could be wrong. But rather than guessing, you could optimize the time interval. Find t, the time interval, such that dF/dt = 0, where F is some function that...

That what? That reflects the efficiency of the market? That minimizes some measure of the turbulence in the market? That minimizes the incentive for high-frequency trading? Some combination of all of the above? What's the right measure of success for this?

Is an HFT arms race necessarily a bad thing? Doesn’t the market in general benefit from these firms viciously competing to grind out spreads+inefficiencies?

I know very little about HFT, but it seems like we’ve gone past “peak HFT margins”. With the Virtu+KCG merger, firms like Jump doing microwave stuff, it seems like return on assets for these firms could have already peaked.

The authors address this in a few places. The gist is that arbitrage became much faster but not more efficient. Here’s a summary from page 6:

> The usual economic intuition about obvious arbitrage opportunities is that once discovered, competitive forces eliminate the inefficiency. But that is not what we find here. Over the time period of our data, 2005–2011, we find that the duration of ES-SPY arbitrage opportunities declines dramatically, from a median of 97 milliseconds in 2005 to a median of 7 milliseconds in 2011. This reflects the substantial investments by HFT firms in speed during this time period. But we also find that the profitability of ES-SPY arbitrage opportunities is remarkably constant throughout this period, at a median of about 0.08 index points per unit traded. The frequency of arbitrage opportunities varies considerably over time, but its variation is driven almost entirely by variation in market volatility. These findings suggest that while there is an arms race in speed, the arms race does not actually affect the size of the arbitrage prize; rather, it just continually raises the bar for how fast one has to be to capture a piece of the prize.