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JTDerp


Total Posts: 47
Joined: Nov 2013
 
Posted: 2018-06-03 20:57
Any tips/reference links for a process to estimate market impact in the limit order book as a function of a participant's order-lot size relative to displayed total lot sizes at inside bid/ask?

I'm about to restart trading of STIR futures spreads in an intraday market-making strategy aligned with monitoring the yield curve (usually flat at close). Trying to determine scalability is a big question in the near-term - going into Size Pro Rata matching engines on ICE Europe/LIFFE for the more liquid markets...curious as to how a trader might estimate an upper limit for his orders before slippage, 'spooking' other traders, order book rebalancing etc. would come into play...

"How dreadful...to be caught up in a game and have no idea of the rules." - C.S.

ronin


Total Posts: 343
Joined: May 2006
 
Posted: 2018-06-12 12:51

I wasn't going to reply given that my experience with STIRs is pretty limited, but given that you got zero responses so far...

As far as I know, your order 1 risk in pro rata orderbooks will be adverse selection. The asymmetry between good fills and adverse fills increases super-linearly with size. I.e. adverse fills are linear in size, but good fills are not.

Slippage and orderbook flows would definitely be second order effects. I wouldn't worry about them until you have sorted adverse selection.

"There is a SIX am?" -- Arthur

gaj


Total Posts: 25
Joined: Apr 2018
 
Posted: 2018-06-12 15:14
Maybe a stupid question, but why would a market making strategy have any market impact or slippage?

ronin


Total Posts: 343
Joined: May 2006
 
Posted: 2018-06-12 16:27
Anything you do in the orderbook has impact.

If you add liquidity, a liquidity taker won't go in as deep as they would otherwise. If you take liquidity out, a liquidity taker will go in deeper than they would otherwise.

Look up the case of Nav Sarao. He was extradited to the US for supposedly causing the flash crash. By placing some orders in some orderbooks. The orders never got filled. The fact that they never got filled was the key element of the indictment.

The specific case for causing the flash crash is 100% nonsense, but it isn't built on nonsense. It is just blown out of all proportion.

Also, market making strategies do cross the spread when they have to. Ususally to lay off inventory or to hedge, but it could be for a number of other reasons.

"There is a SIX am?" -- Arthur

EspressoLover


Total Posts: 334
Joined: Jan 2015
 
Posted: 2018-06-13 16:37
Never traded STIR or pro-rata, and this is pretty much just a random musing, but here's my 2 bps...

Gonna assume you have some sort of decent order book simulator that accounts for previously consumed liquidity. When you simulate with increasingly larger portfolio sizes, at what point do you observe the "elbow", where PnL starts leveling off?

That's probably not too far off from your actual scalability limits. It doesn't account for how your displayed size will affect the other participants. But pro-rata makes the game theory fairly straightforward. Assuming the other liquidity providers are about as roughly informed and rational as you, then the point where you get decreasing marginal returns from adding more liquidity to the level is also about the same point for them.

In FIFO queue this logic doesn't really hold, because every order's in a different position in the queue. But with pro-rata your behavior is mostly fungible with the other participant's behavior. (Unless there's huge discrepancies between participant's models, infrastrucutre or costs)

Good questions outrank easy answers. -Paul Samuelson

JTDerp


Total Posts: 47
Joined: Nov 2013
 
Posted: 2018-06-18 04:20
Much appreciated on the responses, gentlemen. EL, there is tick-level logging of the market transactions, but we have not yet simulated with increasing size.

When I traded these prop in 2012 (which wasn't the greatest of times given Greece's 2nd bailout and the markets were spooked a bit), order size for each trader was capped at a 10 lot per-spread-per-market, and no more than 30 in-total across the several expirations/contracts for that market (modest operations). Once some results are obtained on simulation of the 'elbow' and some measure of adverse selection as Ronin mentioned, I'll post results here.

"How dreadful...to be caught up in a game and have no idea of the rules." - C.S.

gaj


Total Posts: 25
Joined: Apr 2018
 
Posted: 2018-06-27 12:20
This is actually an interesting exercise. As a simplified model, you're basically optimizing:

x / (total_quantity + x) * good_fill_rate - x * adverse_fill_rate

Once market maker A adds an order of size x_optimal, the total quantity changes. Then MM B optimizes this again and adds a new order. MM A's size is no longer optimal, so MM A has to adjust. Then MM C also jumps in. And so on.

The Nash equilibrium is when x_optimal = 0, which happens when total_quantity = good_fill_rate / adverse_fill_rate. So in this idealized, competitive world, you have a fixed optimal total quantity and all market makers should have size = optimal_total_quantity / num_market_makers.

I wonder what happens if num_market_makers > optimal_total_quantity. I guess speed starts to matter since you have to be the first N people to send the order, even then you can only add 1 lot. Anyway, I hope this is not total nonsense. I'm curious what you find in real market data, JTDerp.

ronin


Total Posts: 343
Joined: May 2006
 
Posted: 2018-06-27 14:22
@gaj, it's definitely not nonsense.

I do think you have the units slightly wrong. Your first term is dimensionless, and the second term has units of quantity. You probably want the first term to be

x * x / (total_quantity + x)

x / (total_quantity + x) being the pro rata part, and then you multiply by x again to get the expected quantity conditional on good fill.

It's a good attempt, but probably not the best way to look at it. The good fill rate already incorporates the pro rata element, so it is not really clear how you would measure your "reduced" good fill rate. Is it just the number of hits on the price level? In what time interval? And that's not me being pedantic, it actually goes to the core of what you are doing.

Also, you are assuming the move is symmetric after a good fill and adverse fill. That is probably quite aggressive.

In reality, quoting becomes unprofitable long before there are more market makers than optimal total quantity. So that limit wouldn't be reached in reality.

But speed does matter for other reasons. The first to quote into a level has first priority, and everybody else is pro rated. So there is a legitimate strategy chasing speed without bothering with large quantity.


"There is a SIX am?" -- Arthur

Strange


Total Posts: 1438
Joined: Jun 2004
 
Posted: 2018-06-27 16:04
@ronin - "adverse fills are linear in size, but good fills are not."

It make sense that in a pro-rata book, the adverse fills become dominant as the order size grows. The ultimate adverse move is someone sweeping everything, so that's the limit of this relationship. However, it's not clear to me that it would have to be a linear relationship, do you mind elaborating on this?

I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?'

gaj


Total Posts: 25
Joined: Apr 2018
 
Posted: 2018-06-28 02:58
@ronin

The first term should be multiplied by the size of the uninformed order. Obviously the formula is oversimplified. The proper approach is to use a calibrated exchange simulator as EL suggested.

In any case the game theory implications still stand. All MMs must optimize for f(x)=expected pnl of adding an order of size x.

I realized a couple of points that were missing in my argument. First, x_optimal could be negative, which means the MM that already has an order in the book must reduce his size, but nobody else should add a new order. Secondly, the first MM could just send a single order of size = optimal_total_quantity. This is a Nash equilibrium and the optimal action for the other MMs is to do nothing. Unless they want to screw the first MM.

In practice I think all MMs have different valuations, different inventory, and different adverse fill models, so the game theory is much more complex. Took a quick look at a STIR order book. Only the top of book has decent size as expected, since there is no incentive to quote the levels behind. Looks like there are only a couple of market makers quoting decent size.

ronin


Total Posts: 343
Joined: May 2006
 
Posted: 2018-06-28 15:23
@strange,

That is one of those bits where pro rata behaves differently from price time. In pro rata, everybody is encouraged to quote more than they want, so they get pro rata fills. So the touch is very fat on both sides, and the price doesn't oscillate around at all. It just sits in one place, then moves to a different place where it sits for the rest of the day.

So what I'm saying is that the limit of being run over is pretty much the main form of adverse selection in pro rata. And that is, modulo all sorts of caveats, 100% fill rate.


@gaj,

I agree, your argument is solid.

Here is another way to think about it.

If you quote very small sizes, you get zero good fills (your pro rata share is less than one contract) but you still get adverse fills. So your pnl is negative.

In the other limit, if you quote too big, one adverse fill blows out all your good fills. So your pnl is again negative.

Somewhere in between, there is the optimal size to quote. It depends on the total quantity, and everybody changes it by adding and removing liquidity.


"There is a SIX am?" -- Arthur

Strange


Total Posts: 1438
Joined: Jun 2004
 
Posted: 2018-06-29 01:02
LOL, I was being dense. I was going to argue that taking out of the full level should follow some form of poisson process, but now I see what you mean - it's linear with respect to your order size :)

I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?'
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