# SDE simulation: P or Q?

Let's take a GBM under $P$:

$dS=\mu dt+\sigma dW_{t}^{P}$

and then under $Q$

$dS=r dt+\sigma dW_{t}^{Q}$, where $dW_{t}^{Q} = dW_{t}^{P} + (\mu - r)/\sigma dt$

Now, let's say that I have calibrated my model on the mkt option prices (using B&S) getting the parameters that i need. Question:

Do I have to simulate the path subtracting from $W^{Q}$ the market price of risk? Or what i only need is a brownian motion (knowing that $r$ in the drift part is already the result of the change of measure)?

Thanks.

-
You only need Brownian motion. –  Rustam Oct 17 at 7:12