Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Friday, June 10, 2011

Flash crash the nat gas!

As shown on posts on Zero Hedge, (correction, these are originally from Nanex) there have been some bizarre patterns in the trading of natural gas in the past couple of days. The charts below are from the evening of June 8, 2011 and come from the first of the two articles linked above:

At first glance this looks like nearly perfect chaos.

The last figure represents a one-dimensional projection of a Lorenz butterfly curve, shown in its glory below.

In reality the trading data isn't as nice as it first appears. There has been a bit of playing around with the time axis on the first two plots. I have subsequently digitized the data with trades at half-second intervals (but I'll outline the caveats below).

The axis on the bottom is time in seconds, starting from 19:40:37 on 08-Jun-11. The digitization is at half-second intervals, because the analysis below requires evenly spaced data. There were some difficulties, however. There was not always a trade right on the half- or full-second mark. Frequently the two nearest trades on either side of the desired time interval were at the same price so that it would be reasonable to use that price. Sometimes, however, the two nearest prices were quite far apart--for these I used a midpoint between bid and ask at the moment--however arguably this is not a price, particularly when we observe that many trades took place either above the ask or below the bid. Additionally, there are intervals where the midpoint between the bid and ask is actually undefinable, as during the interval from 19:42:04 to 19:42:06 where the bid price fluctuates in a complex fashion while the ask remains constant. So there are risks in this analysis.

The two dimensional lagged state space (using a 2-s lag to minimize mutual information) looks as below:

Not quite as beautiful as the Lorenz butterfly curve. I smoothed the data through a 3-point moving average filter as the original really looked like hell. The sinusoidal waves that slowly increase in size are reflected in the two-d state space as a spiral, drawn from the centre outwards, until the curve flies off into a new area of phase space.

The conventional dynamic explanation of the nat gas trading curve would be of a system in equilibrium--but the equilibrium is unstable, and the wobbles get progressively larger until the system shifts to a new equilibrium. Such a dynamic interpretation is incorrect. The Lorenz equilibrium is all equilibrium. What we perceive as a sudden shift in equilibrium is actually part of the equilibrium state.

Disequilibrium--it's new equilibrium.

From a trading perspective, the nat gas trading is more straightforward. Someone is able to profit from variability. The proper positioning of puts and calls may allow you to benefit by a large move (either up or down) in the price of a stock or commodity. After that, you can try to hit any buy or sell stops if you are able to drive the price up or down, (or in this case, both ways, until the sell stops were hit triggering a cascade in price). If there had been more buy stops, then the price would have melted up. It was simply a matter of luck that the price melted down.

As in all markets there are two (or more) participants. Leaving the actual trades for a minute and scrutinizing the fluctuations in the bid and ask, we see a complicated psychological game being played. I see many of the tricks that I have seen in thinly traded gold stocks priced by a market maker. You see the bid (or trade price) creep up towards the ask price, then run away, perhaps hoping to draw the ask price down.

But the time frame is completely different. I used to see this play out over the course of a trading day (my favourite was when I would get a partial fill of, say 500 shares of some penny stock before the price would swing away, and could imagine the market maker saying "do you want to pay full transaction fees for a $100 sale, or are you going to meet my price and fill your order?"). In this case, these games are being played on a split-second scale.

Game theory has been digitized and is running on a level of complexity that leaves TIT FOR TAT in the dust. Unfortunately my textbook on the subject is being used by my seven-year-old, so I can't get into strategy games between different players.

Many of the price rises happen while trades are occurring above the ask price. How does that happen. Is the asker crossing transactions with fictional entities to lure the buyer? Similarly, many trades occur below the bid price as the price is falling. Are these fictional crosses? Are these real trades or just a gimmick to lure in another party (hurry up and buy--look how fast price is falling!).

The chaotic appearance of this function is simply an emergent property of the gaming algorithms.

Lastly, I will point out that my analysis is roughly seven orders of magnitude slower than the frequency of some of the trades.

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