Now let us extend these concepts just discussed for the case when we have the figure given as

Figure 10.11: A stock and its increase and decrease of price

For the Figure we select  and  to be small, such that  (a constant), and this  is variance per unit time. Hence it turns out that this random walk converges to a Brownian motion as .

Thus:   where  and  have their usual meaning.

Using Taylor series expansion we get .
Which results in
                                                                 

Now when time is taken as 1 we have the following , as true. In the general case when the time period is , the equation takes the following form which is

                                        .