Does anyone know how to find the probability law (distribution) under P* of a Black Scholes Call Option price $C_t$ for $0 < t < T $?
(Under P*, $ dC_t = \frac{\partial c}{\partial s}\sigma S_t dW_t^{*} + rcdt $, where $C_t = c(s,t)$, $t \in [0,T]$ )
I'm expecting it will not be geometric Brownian motion but I'm not sure how to prove it.
Thanks!