## The **MATH** behind the random walk of stocks

We are looking at a percentage wise change of the stock values. Let us say the stock
*S* changes by some amount D* S*
in the time interval D* t*.
The relative change is the ratio of the value change and the value of the stock
D* S / S* (You get the change in percents by
multiplying this number by 100).

This ratio is rising continuously by some amount *r* , like the interest on
savings, multiplied by the time interval:

*D S / S = r D t*

In addition you have random fluctuations (so-called Gaussian fluctuations).
If **D x** is such a fluctuation
with a size of +1 or -1 *on the average* we can write the whole equation
for the stock evolution as follows
*D S / S = r D t +
s D x*

The parameter *s* is the strength - or
amount - of the fluctuation during the time span *D t*.
* s * is the volatility of the stock. This equation determines the change of the
stock value with time.

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