# definition for “the viscosity” in financial market data series

I am willing to calculate and monitor the evolution of extreme-viscosity in the financial markets data series.

Wikipedia says "Put simply, the less viscous the fluid is, the greater its ease of movement ". So rather than looking for the mighty viscosity should I simply focus on ease-of-movement? Well, the "ease of movement - (EOM)" is a catchy phrase since there is a well known indicator with the exact same name. That EOM indicator is defined in investopedia as: "A technical momentum indicator that is used to illustrate the relationship between the rate of an asset's price change and its volume. This indicator attempts to identify the amount of volume required to move prices."

In elementary school mathematics it is as simple as: EOM = (Close of today - Close of yesterday) / Volume

Do think "extreme viscosity can be monitored by the extremes in EOM"... Or would you suggest something else to calculate viscosity?

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Did you make up this concept yourself? Is there any source for the use of the term "viscosity" in a financial context? – Tal Fishman Apr 25 '12 at 18:17
Dear Tal, There are lots of things that I made up but this is not one of them. When asked about viscosity in financial data series the first book that comes into my mind is "An introduction to econophysics : Correlations and complexity in finance - Rosario Mantegna & Eugene Stanley". – Sts Apr 26 '12 at 8:39
I see where they use it as an analogy, but it still looks like they do not directly apply the terms "viscosity" or "ease-of-movement" to financial time series. Also, your definition of ease of movement seems arbitrary. I do not understand why you would look at the absolute price change divided by volume. Also, since no trading takes place overnight, perhaps you should look at close - open? Perhaps look at log price changes? Perhaps log volume, too? – Tal Fishman Apr 26 '12 at 14:53

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You can measure whatever you want...there is no standard definition of viscosity in financial mathematics. Most stochastic modelers would take it to mean terms involving $\nabla^2 V$ in the associated Feynman-Kac PDE, which is clearly very different from the simple heuristics you have in mind here. – Brian B Apr 26 '12 at 17:35

## 2 Answers

Using intra-day data, the concept of viscosity is easier to define. At the microstructure scale, you can see the price moves as a diffusion constrained by the quantities in the order books. Viscosity is a mix of pressure of volumes, rounding by the tick size, and bid-ask bounce.

See for instance A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones, by M Rosenbaum and C Y Robert, In Jnl of Financial Econometrics Volume 9, Issue 2, pp 344-366. In this paper, authors present a way to estimate simultaneously the volatility and a rounding adjustement level $\eta$ (eta). This parameter can be seen as the viscosity of the studied stock.

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A standard definition of "viscosity" is "stickiness. The MORE viscous something is, the LESS ease movement.

So "viscosity" in this context would refer to the "stickiness" of one price compared to another in a time series.

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Dear Tom,  Thanks for the "English" definition. I will use the term stickiness since it is more understandable. But I would be glad if you can suggest a "mathematical" definition too. – Sts Apr 26 '12 at 8:50
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