Geometric Brownian Motion

The most important thing to know about geometric Brownian motion is that it is by definition a random, or stochastic process. Specifically, the logarithm of the stochastic quantity must be said to follow Brownian motion. This process operates within continuous time as opposed to being discretely valued, and it will have an element of drift associated with it.

The second most important thing to know from the perspective of finance is why we prefer use it. Brownian motion by itself allows for negative values, which is obviously not desirable if we are attempting to directly model most asset prices (stocks in particular) as negative asset prices are most uncommon. Hence, we use the geometric Brownian motion and can then utilize a logarithm to return back the Brownian motion itself without using a model that results in negative asset prices.



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