Hi,I am studying the GBM and I wonder me which is the rationale behind the fact the this model is able to generate only positive prices.I know that the solution of the GBM is distributed according a lognormal distribution and so the solution must be positive to retrieve the normal process associated. But if I look the GBM SDE I don't realize immediately this feature....Thank you very much.....

The SDE can be exactly solved and the solution has the form S(t) = S(0) exp( blah)Regardless of what 'blah' is, since e^x > 0, the solution will be positive if S(0) is.

It is not easy to see why the solution must be positive by looking at the GBM SDE...... you'd better look at the solution directly.

QuoteI am studying the GBM and I wonder me which is the rationale behind the fact the this model is able to generate only positive prices.Only if the initial price in positive...QuoteI know that the solution of the GBM is distributed according a lognormal distribution and so the solution must be positive to retrieve the normal process associated. But if I look the GBM SDE I don't realize immediately this feature....Here is an intuition: Say we start with a positive price. If at any time, the price drops to zero, it should stay there because dS is proportional to S. So, to get to a negative value, it must 'overshoot' the value zero which is not possible because the process is continuous.