# Question about the process of monte carlo simulation

I have encountered an interesting question. Is it better to simulate the geometric brownian motion process for call itself or GBM for the underlying.

My question is can we actually apply GBM to call? is it possible?

• The call price does not follow a geometric Brownian motion when the stock price does. We have $\mathrm{d}C_t = \frac{\partial C}{\partial t} \mathrm{d}t + \frac{\partial C}{\partial S} \mathrm{d}S_t + \frac{1}{2} \frac{\partial^2 C}{\partial S^2} \mathrm{d} \langle S \rangle_t$. So simulating the callprice does not work if our aim is pricing as the dynamics depend on its unknown derivatives. Or did I misunderstand your question? – LocalVolatility Dec 26 '17 at 13:36