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?
LocalVolatility's comment is correct. Just to provide a reference, the below is from Monte Carlo Methods in Financial Engineering by Paul Glasserman:
"Valuing a derivative security by Monte Carlo typically involves simulating paths of stochastic processes used to describe the evolution of underlying asset prices, interest rates, model parameters, and other factors relevant to the security in question."
The general idea is to assume the underlying price follows GBM and then simulate many price paths.