Hi I am pricing an option using GOP as numeraire. i havevalue of the option at time t is V(t) = S*(t) E{ V(T)/S*(T) | F(t)}where: S* is the GOP, V(T) is a well-defined payoff of the option at maturity T and F(t) is filtration up to time t and expectation wrt real world probability measure P where assets discounted by the GOP are martingale.this info is irrelevant but just to provide context: my economy has three assets with well defined dynamics: riskless bond B, and two risky GBM assets S1 and S2 my option payoff at T is whatever, say Margrabe option (S2-S1)+my question is the following: i know parameters for B, S1 and S2 hence i can calculate the composition of GOP. now that's great, but the formula for the value of the option has S*(t) i.e. the value of the GOP at time t. how do i know this value of the GOP? am i doing something really stupid? am i supposed to get rid of S*(t) somehow and work with the ratio S*(t)/S*(T)?O.othanks!!!

It's the ratio that matters, so you can safely set S(t)=1 and S(T) to be the time T value of one unit of currency invested in the growth optimal portfolio at time t.

worked out thanks)))

Very interested in GOP and the benchmark approach in general: if you have anything you would share i'd be interested in thoughts/ideas/...Srioae