The physics of the bag

To describe in a useful way a system that consists of a big number of particles one must be appealed to statistical procedures. The gases are a classic example. One liter of any gas in environmental conditions — for example, the air one spring day — contains the fortune of approximately 20.000 trillions of molecules: to want to describe it studying the behavior of each of them is practically impossible. To achieve it there are used statistical methods that allow to obtain relations between the properties of the individual molecules, like the energy and the speed, with the properties of the gas like everything, this is, his pressure, temperature …

The study of the behavior of the gases, realized by the physicist and mathematician German Ludwig Boltzmann in 1877, put the bases of a branch of the physics called physical statistical. Without her nowadays it would be an impossible comprehension sew so dispa¬res like the internal structure of the stars or the superconductors.

The statistical physics has multitude of applications but the most spectacular is his use in economy. On having heard one, he can wonder what relation can be between the behavior of the gas of a gas cylinder of butane and the evolution of the interest rates. It is possible that we see it clear if we analyze the movement that realizes an any molecule in the air. This molecule is subject to such a number of influences, principally clash with other molecules of the air, which is impossible to predict the direction in which it is going to move. This is the brownian movement discovered at the beginning of the XIXth century for the Scotch botanist Robert Brown, and it constitutes the best sample of erratic movement.

The stock market also is subject to a very high number of influences, unpredictable all of them, which it makes impossible to foresee his future evolution. Can a relation be established between both disciplines? Yes. In 1900 the French mathematician Bachelier discovered that the fluctuations of the bag could be described using the theory of the brownian movement. In particular, he proposed a formula to fix the price of an option being based on the idea of that such fluctuations were following the same process as a molecule moving inside an any gas.

This work remained forgotten until the 70s, when the scientists Black and Scholes introduced the methods of the statistical physics to describe financial activities as the market of options. Since then we have been present at a renewed interest in this curious relation. Up to that moment one was depending on the 'smell' and subjective analysis of the economist; now he already prepares of objective hardware to study them.

Truth that it turns out to be fascinating to discover that the study of the behavior of a gas serves to evaluate the risks which a bank faces on the world market?