Random Walk

You can simulate a stock price by using the idea of a random walk.
One of the simpliest ways to obtain a random process is to use tossing a coin.
As a simple experiement start with the number 100 which you can think of as the price of the stock.

If you throw a head then multiple the number by 1.01
If you throw a tail then multiple the number by 0.99

Continue this process for 20 throws and plot the graph of the stock price.

Instead of physically tossing the coin you could use the Excel function RAND() to generate a uniformly distributed random sequence of 1's and 0's.

Notice in this experiement that I have chosen to multiple by 1.01 and 0.99 instead of just adding +1 or -1
This is very important because as the asset price increases so does the change from one day to the next.
Therefore it makes more sense to model the price changes as being propertional to the current price.

It is important to model the return on the asset (i.e. its percentage change) rather than its absolute value.

Lognormal Random Walk

If we use the multiplication rule we get a lognormal random walk
Also known as a Geometric Random Walk

Normal Random Walk

If we use the additive rule we get a normal random walk
Also known as Arithmetic Random Walk

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