Simple Random Walks

It was noted early on that the markets resemble to random processes. Thus we could try to simulate a market with an appropriate random processes.

A simple such random process is the Random Walk, for which we take equal size "steps" either increasing, or decreasing a security's value in random (for example with a 50% probability for either way). After several iterations we could get the probability distribution of the price of the security over time.

To have a better idea of how random walks look like, a simple Random Walk model applet is available [here].

Hurst Random Walks

An improvement of the random walk is the biased (hurst) random walk. Specifically, we change "step" direction with either a lower (in our case) or a higher probability. This way we can simulate the market even better, as it is more likely for a trend to continue for the next day.

For our random walks, a hurst exponent of 0.57 is used. This means that for each step of the simulation we change step direction with a 43% probability. The use of this particular value is a result of a CSE691 project on random walks by G. Longo, which can be found [here].