“But there are several aspects of the quantitative approach to finance, and no single one of these aspects, taken by itself, should be confounded with financial econometrics. Thus, financial econometrics is by no means the same as finance statistics. Nor is it identical with what we call general financial theory…Not should be financial econometrics a synonymous with the application of mathematics to finance. Experience has shown that each of these three view-points, that of statistics, financial theory, and mathematics, is a necessary, but not sufficient, condition for a real understanding of the quantitative relations of modern financial life. It is the unification of all the three that is powerful. And it is this unification that constitutes financial econometrics.”

This paragraph is a virtual copy of the one in p. 2 of Frisch’s Editor Note on Econometrica Vol. 1, No. 1.The only difference is that economics has been replaced by finance, economic by financial, econometrics by financial econometrics. It was written 74 years ago but it fully reflects the spirit of this special issue.

High frequency finance is an archetypical example of Ragnar Frisch’s words. It represents a unification of (1) financial theory, in particular market microstructure, (2) mathematical finance, exemplified in derivative markets, and (3) statistics, for instance the theory of point processes. It is the intersection of these three components that yields an incredibly active research area, with contributions that enhance the understanding of today’s complex intra-daily financial world.

“Theory, in formulating its abstract quantitative notions, must be inspired to a larger extent by the technique of observations. And fresh statistical and other factual studies must be the healthy element of disturbance that constantly threatens and disquiets theorists and prevents them from coming to rest on some inherited, obsolete set of assumptions.”

The New York Stock Exchange has a group of liquidity providers called supplemental liquidly providers (SLPs), which attempt to add competition and liquidity for existing quotes on the exchange. As an incentive to the firm, the NYSE pays a fee or rebate for providing said liquidity. As of 2009, the SLP rebate was $0.0015. Multiply that by millions of transactions per day and you can see where part of the profits for high frequency trading comes from.

The SLP was introduced following the collapse of Lehman Brothers in 2008, when liquidity was a major concern for investors.

It's no longer computers trading with institutions. We've now entered the second generation of HFT. It's computers trading with computers.

Think about it this way...

You program your computer the old-fashioned way. You're willing to buy stocks if the S&P futures hit a certain premium to the cash index, and you're willing to sell stocks if the futures fall to a significant discount. I know your trading parameters, and I see your orders before anyone else. So I program my computer to jump in front of your trades, thereby preventing the market from reaching the extremes at which you're willing to buy or sell, and then forcing you to chase a position. Or in a low-volume environment, I allow you to get into position then use my bankroll to pressure prices against you. I run your stop orders and force you out of position and then let the natural forces of the market run the other way.

This is what created the remarkable one-way action to the downside we saw back in March. And it's what is happening to the upside right now. The natural ebb and flow of the market is changing. It's no longer two steps forward then one step back. It's more like 100 steps forward then 20 steps back, or 100 steps back then 20 steps forward. In other words, thanks to HFT, the trading ranges are extended. Regulators are now looking into ways to reduce the effects of HFT. But they're so far behind the curve, any new laws they come up with will be antiquated before they're passed.