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Preventing Market Bubbles

December 4, 2013

The simple market model of supply and demand was always reassuring. When people need much more of something, driving up prices, equilibrium forces would work to generate a greater supply. Today's markets, however, are quite a bit more complex.

In the past, everyone knew how much an apple should cost, the price being not that much different this year than last. In contrast, faulty valuation of something unfamiliar, such as the initial public offering (IPO) of an Internet company, can lead to huge upstream corrections in valuation and a market bubble.

With money moving at the speed of light, at least the slightly reduced speed of light in fiberoptic communications cables, a regulator's ability to control a market firestorm using tools such as a trading halt or trading curb is severely limited. A regulator would have a fighting chance if a model existed that could predict a market bubble.

The New York Stock Excahnge in 1909The New York Stock Exchange in 1909, when money still traveled at the speed of ink.

(Scan of a postcard, via Wikimedia Commons, modified to remove captioning.)

When chaos was discovered, people got the idea that the stock market might be chaotic.[1] Although we can cite much anecdotal evidence, this idea is not proven, since the stock market is not a typical experimental system. There are, however, quite a number of scientific papers written about the idea, such as the ones cited as refs. 2-3.[2-3] Large events in most systems follow a scale-free (power law) probability distribution, so extreme events are not predicted.

A recent paper in Physical Review Letters notes the similarity between extreme, catastrophic events, such as market bubbles, and the performance of a system of coupled chaotic oscillators.[4-6] What's interesting in this paper is the presentation of a model that forecasts an impending extreme event. What's more interesting is that the forecasted extreme events can be suppressed by application of small perturbations to the system.[4-5]

The authors presented the design of their chaotic oscillator system in a previous article.[7] This circuit, and its response, is shown in the figure.

Figure caption
Chaotic oscillator circuit and its response. Component values are as follow: R1 = 46.50 kΩ, R = 14.86 kΩ, R2 = 14.85 kΩ, RE = 14.86 kΩ, RL = 512 Ω, R3 = 14.85 kΩ, C1 = 0.01473 μF, C2 = 0.01483 μF, C3 = 0.01483 μF; D1 and D2 are 1N4148 diodes; the operational amplifiers OP1 and OP2 are LF411CN. The circuit is driven by a four volt, 770 Hz, sine wave. (Image sources: Left, fig. 1, and right, fig. 3, from ref. 6, via arXiv.[7])

The central prediction problem, as summarized in the power density function shown below, is that extreme events should be rare; but, every so often a killer event, termed a "Dragon King" by the research team, arises. The Dragon King concept was explained by coauthor, Didier Sornette, at a recent TED conference.[8]

Power density function for market events.Power density function for market events.

The x-axis is the largest peak value within a burst.

(Fig. 2 of ref. 5, via arXiv.[5])

Didier Sornette, who is with the Swiss Federal Institute of Technology, is director of the Financial Crisis Observatory, a group whose goal is the prediction of such market disturbances. His coauthors on this study are Dan Gauthier, a professor of physics at Duke University, Gauthier's former postdoc, Hugo Cavalcante, now at the Federal University of Paraiba (Brazil), Edward Ott of the University of Maryland (College Park, Maryland), and Marcos Oria from the Federal University of Paraiba.[6]

Gauthier has been doing experiments with chaos-generating electrical circuits, such as the one shown above, since the 1990s.[6] When identical such circuits are coupled, they will synchronize when there is tight coupling of the circuits, but a lighter coupling will allow excursions in the phase space trajectory of one oscillator with respect to the other.

During an experiment, the chaotic trajectory will visit a region of phase space at which an extreme event might occur. In such a region, the circuits will temporarily lose synchronization, leading to mostly small changes, but sometimes a very large change, similar to a market crash. Most disturbances follow a power law distribution, but the extreme events deviate from it.[6]

The research team found that they could prevent such "dragon kings" if they applied a small signal to one of the circuits at just the right time. Says Gauthier, "Maybe tiny nudges can make a big difference," but he adds,
"The limitation of our paper is that we haven't shown that our circuit has relevance to the stock market... We aren't yet sure where to look, but for this one simple system, we figured out how to find it."[6]
It's hard to publish in Physical Review Letters, and this paper was no exception. Gauthier says that the team needed to allay the concerns of a difficult team of reviewers before it could be published.[6] The research was funded in part by the U.S. Office of Naval Research and the Army Research Office.[6]

References:

  1. Tom Konrad, "Chaos Theory, Financial Markets, and Global Weirding," Forbes, August 30, 2011.
  2. Taisei Kaizoji, "Speculative bubbles and fat tail phenomena in a heterogeneous agent model," arXiv Preprint Server, December 19, 2003.
  3. Sorin Vlad, Paul Pascu and Nicolae Morariu, "Chaos Models in Economics," arXiv Preprint Server, January 20, 2010.
  4. Hugo L. D. de S. Cavalcante, Marcos Oriá, Didier Sornette, Edward Ott and Daniel J. Gauthier, "Predictability and suppression of extreme events in a chaotic system," Physical Review Letters, vol. 111, no. 19 (November 8, 2013), Document No. 198701 (5 pages).
  5. Hugo L. D. de Souza Cavalcante, Marcos Oriá, Didier Sornette, Edward Ott and Daniel J. Gauthier, "Predictability and suppression of extreme events in complex systems," arXiv Preprint Server, September 13, 2013.
  6. Market Bubbles May Be Predictable, Controllable, Duke University Press Release, October 17, 2013.
  7. Gilson F. de Oliveira Jr., Hugo L. D. de Souza Cavalcante, Orlando di Lorenzo, Martine Chevrollier, Thierry Passerat de Silans and Marcos Oriá, "Tunable power law in the desynchronization events of coupled chaotic electronic circuits," arXiv Preprint Server, September 12, 2003.
  8. Didier Sornette, "How we can predict the next financial crisis," TED, June, 2013.