Stock Rates

I have here a series of three random walks. Which one would you rather call a stock rate. The following?

black-swan-distribution-002And would you say, it is biased? Most likely, you would. In fact, it is not. It is a random walk with 0-1-normal distributed steps.

How about the next one?

black-swan-distribution-011Does it look more realistic? I like the fact, that is has these jumps. The steps here have a distribution with density 1/(1+x^3), which is Talib’s power law with exponent 2 (the Black Swan Talib from my previous post). Then the probability of taking a step larger than a tends towards 0 like 1/a^2. This distribution has a definite expected value, but the variance is infinite.

If we make this more extreme (power law with exponent 1), we take the density 1/(1+x^2), we get a distribution with undefined mean value. Here is a simulated random walk.

black-swan-distribution-008We get normal behavior, and suddenly an outbreak of immense size. It is close to the turkey story in the book. The turkeys are fed well for a long time. They come to the conclusion that things are stable, and then all of a sudden …

The graphs and simulations were done with my Euler Math Toolbox. See the link on the link bar.

Ein Gedanke zu „Stock Rates

  1. Mark, New Hampshire

    The second one is a stock rate – it is a more reasonable likeness to the rate at which the market rise and fall.

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