Comment by _delirium | Hacker News Reader

Comment by _delirium | Hacker News Reader

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How about rather than adding regulations, just discretize the market's clock? Would a market that performed a trade-resolution tick once every 100ms lose anything important? I believe arbitrage improves efficiency, but I'm less clear on the benefits of extremely high temporal resolution. Currently that's what the incentives encourage optimizing for, among other things. If you predict a market movement 10ms ahead of time, you can profit from that brief 10ms temporal-arbitrage window. And like any arbitrage, that does indeed improve the pricing signal in an absolute sense, in this case by taking a price change that was 10ms later than it "should've been", and moving it up in time via your trading. But it's not clear that 10ms-level pricing inefficiencies are actually something particularly important to smooth out via arbitrage, when you can just define them out of existence by going to a discrete-time market (which are fairly well-studied in the mathematical literature).

I think if you consult the literature you'll find that the prevailing trend is for markets to become more continuous rather than more discrete. Continuous markets help with true price discovery. Our markets are continuous in time right now and we've pretty much squeezed the spreads to their maximum, so while prices aren't continuous they are about as close as we can get w/o eliminating the profitability of the primary market participant (market makers) that make it function.

You can scheme up any number of possible microstructures that sound interesting on the surface. There's a reason why none exist. Remember, there is nothing to stop you from implementing a time-discretized market place. Current regulations (Reg-ATS) allow for you to do so. You'll find it hard to compete. Some markets do perform large scale discretization for block orders. Read up on POSIT and related ATSs and dark pools.

I read somewhere that non-hft tend to trade much more at the "second" tick. This may have been b/c they were dumb (hard to believe) or because converging at the same time (15:30:10 instead of 15:30:10.175) gives them better chances to finding a match to their sell/buy position

FYI - I wrote the successor to posit. Point in time matching goes out of fad when volatility increases. Why take on the risk of executing a block at a single point in time when you can spread that risk out over the day?

Evidently you have childlike trust in the capacity of the second-tier Russian mathematicians and physicists to get the boundary conditions right.

what exactly is 'true price discovery' ?

can a price be false?

With insufficient trades, you cannot know if a certain price is really what the 'market' wants to pay, just what that one person at one point in time wanted to pay. Overgeneralized, the more trades, the more accurate the price gets.

Discretization often leads to instability, particularly if not done carefully. The prototypical example is naive discretizations of stable ODEs. Of course, all we have are toy models and speculation. The only real way to know is to try it.

If I remember right, a couple of Asian equities markets have some sort of "auction on clock tick" mechanism, so we might be able to look to their experiences.

> Discretization often leads to instability ...

> Of course, all we have are toy models and speculation

These two statements could be construed to be in conflict, especially as I haven't the faintest idea what naive discretizations of stable ODE's is, and Google isn't of much assistance in providing an explanation that I can digest.

I didn't intend them to be in conflict - I listed a toy model, and acknowledged the limitations of it.

An explanation of ODEs and instability (some math background is obviously required): https://en.wikipedia.org/wiki/Stiff_equation

You lead with a fairly strong statement presented as a known fact and then later indicate it's just a model.

To me the idea of slowing things down sounds vaguely sensible, but I also know that I don't know enough to really judge. So it sounds like no one else really knows either, but the entrenched players like things the way they are, which makes sense, because the ones who have the money to be at the table running things are probably also the ones who have the money to throw at HFT and come out ahead.

It is a well known fact about dynamical systems in general.

I.e., if you ask me about the stock market, a flight control system, an electric circuit, a biological system and a computer network, I'll tell you that continuity gives you a better shot at stability than discretization in most of them.

I.e., if you don't know what you are talking about, lean towards continuity. If you do understand things, then explain the mechanics and back it up with empirics.

The hypothesis being advanced by people proposing point-in-time clearances is not necessarily that it will make the market smoother. It's that it will free up a lot of resources for other purposes.

For what it's worth - and not to distract from your real point - Exponential (or the more general Lyapunov) stability are a better explanation of instability. Stiffness is more a property of the method used to solve the ODE, rather than of the ODE itself.

Stiffness is a property of certain dynamical systems, which certain ODE solvers are better suited for. That said, "stability" is an ugly word in numerical methods, particularly for differential equations, as it could mean a number of things. I think this is the source of the confusion here.

It seems that investors trading on an exchange operating at discrete time intervals would be at a arbitrage disadvantage if other exchanges offered continuous trading in the same shares.

So a demand for markets that are liquid and efficient rewards trading that is continuous in time over time-discrete trading, and firms are competing hard to shave milliseconds from latency with co-located hardware and faster trans-oceanic cables.

On the other hand, pricing is limited by regulation to penny increments, with some pressure to telegraph smaller increments.

Are we likely to see a push for trading with offers and trades denominated in milli-cents or micro-cents? Would smaller pricing increments be welcomed by traders or regulators or neither?

Are any markets in the world trading at tiny denominations? (NB: assumes pricing in integer quantities of tiny denominations)

I don't see a reason that "normal" investors would be at an arbitrage disadvantage if trading on an exchange that was discretized to, say, 100ms. Arbitrageurs would still have an incentive to keep the prices on the "slower" exchange in line with the "continuous" exchange's prices, trading at the discrete ticks to exploit price differences. So, price differences past an epsilon shouldn't persist for more than a few ticks, which is more than fast enough for most non-HFT investors, who don't typically make trading decisions with anything close to sub-second precision anyway.

I think a bigger question mark with my admittedly offhand proposal is whether discretizing might actually increase gaming opportunities, since the change could do non-obvious things to the strategy space. On the other hand, it might also remove existing market-gaming opportunities (which are fairly poorly understood, and axiomatically assumed not to exist by the idealized equilibrium analysis economists typically use). Alas, current game-theory solvers don't scale up anywhere close to well enough to give solid answers in either direction (real markets are a bit more complex than 4-participant games iterated over 10 timesteps...).

>I don't see a reason that "normal" investors would be at an arbitrage disadvantage if trading on an exchange that was discretized to, say, 100ms. Arbitrageurs would still have an incentive to keep the prices on the "slower" exchange in line with the "continuous" exchange's prices, trading at the discrete ticks to exploit price differences. So, price differences past an epsilon shouldn't persist for more than a few ticks, which is more than fast enough for most non-HFT investors, who don't typically make trading decisions with anything close to sub-second precision anyway.

Sure, but what you're missing is that the slow exchange's prices are always going to be worse. Not a lot worse - probably only a penny either way on some ticks, and zero on other ticks - but a little. So why would any investor with the choice ever choose to trade on the slow exchange rather than the continuous one?

"Worse" in what sense? Won't the prices deviate pretty randomly around the true price, sometimes behind a penny higher than the continuous exchange, and sometimes a penny lower, making it basically a wash?

No. If the discrete exchange makes it possible to withdraw an offer in between ticks, then the HFT guys would do that every tick - so you actually wouldn't get a price (or you'd get a very wide spread), and it would basically fail to be an exchange. So let's assume any order you have on the book stays there until the next tick's auction. In that case the HFTers are going to give a much higher spread, because if new information comes in at 3.2s and the stock is suddenly worth more than it was at 3s, but they can't withdraw their sell order until 4s, then obviously they lose money. So occasionally you'd get a better price on the discrete exchange (when the market moves further than the spread in the space of one tick) - but the HFTers would be terrified of this situation, and make their spreads wide enough that they think it's impossible. So 99% of the time, you'd get a worse price.

SecondMarket is a start up pushing in this direction. The company whose shares are trading set the trade frequency. Sometimes once per quarter, once per day, whatever they want. Obviously, this is much less liquid.

Yep. One daily cross would be in some ways more fair. But it would also wound price discovery significantly.

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