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Evaporation & Markets, by Victor Niederhoffer

With all the news about excessive water, I thought it would be good to study up on evaporation, the process by which water is turned into gas. Evaporation is the primary force in the water cycle process by which water moves from the liquid state to the atmosphere and then back to the ground. What I learned about evaporation is quite different from what I read in school. It depends on pressure and entropy, for example, as well as the common factors I learned about in school such as wind, humidity, energy and temperature. A good article on this is "Why do things sometimes melt and sometimes sublimate?"

To simplify, Evaporation is going on at all times. Its rate depends on the distribution of molecules and how many are close to speeds necessary to turn them into a gas. (I would be pleased with a more precise market-related simplification.)

I hypothesize that evaporation in the stock market comes when a stock or other market is near a new high or new low and it receives energy from the fixed momentum boys to raise it to new highs or lows. The process provides a net cooling of the stock market, which I analogize to a net reduction in volatility. And when the markets or stocks setting new highs or lows return to the non-extreme parts of their distribution there is an increase in the velocity and temperature of the market.

I hypothesize also that other things that provide evaporation for the market would be sources of heat from political , monetary or weather events. The rate of these process will depend on the volume of trade during the day according to the same principles in the sublimation article.

Someone's going to tell me that I am an ignoramus and clown for trying to draw analogies from this simplification, and that markets are different, and that it's already been done in the area of econophysics or some such, and I tip my hat to them and join them in their critique.

Dr. Kim Zussman comments:

One could also look at the Boltzmann distribution, which describes the kinetic energies of (say) molecules in a beaker of boiling water. None of the molecules are perfectly stationary (absolute zero), and most move at speeds consistent with the overall temperature. However some have energies many times the average temperature, and are much more likely to escape the hydrogen-bonding and gravity holding water in the beaker.

Mr. Ckin adds:

Maxwell-Boltzmann had some particular constraints and assumptions in order to make the curve continuous. Among them, the sample only applied to an ideal gas (not a "sticky" gas in which electromagnetic induction or electronegativity would cause to molecules to interact), all molecules would be in the ground state, and there would be no collisions which would cause an excited state of any molecules. I think that it also assumes cold gases, which would not lose radiation into space.

I remember doing fairly well in statistical mechanics in college, but when I went back to look at my old notebooks, I see handwriting that looks like mine, but the math (differential equations, triple integrals) looks like a foreign language. Nevertheless, statistical mechanics probably has lots of relevant tidbits for financial markets, but when one starts to consider differential equations relating to dynamic systems, keep in mind that there are an infinite number of solutions.

Here's an issue that I have been pondering relating to dynamic systems and moving bodies as they relate to financial markets: Is volatility a mean-reverting quantity? Any sort of volatility measure will do, VIX, VXN, historic, implied, average daily trading ranges, etc. Grant's Interest Rate Observer touched upon this question a few months ago, but with limited reference to any analytical work. Knowledge of the answer would have a meaningful impact on pricing of securities with embedded options such as convertibles and MBS.

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