Assume you have two stocks S and P so that at initial time t = 0: S_0 > P_0. You bought an option which pays off S_T - P_T as long as St > Pt though the time 0 < t < T. What would be the price of such option ?

*I am looking for a non-arbitrage argument avoiding any specific distribution assumptions (log-normal, normal etc) if possible.

Assume you have two stocks $S$ and $P$ so that at initial time $t = 0$: $S_0 > P_0$.

You bought an option which pays off $S_T - P_T$ as long as $S_t > P_t$ through the time $0 < t < T$.

What would the price of such option be?

*I am looking for a non-arbitrage argument avoiding any specific distribution assumptions (log-normal, normal etc) if possible.

Assume you have two stocks S and P so that at initial time t = 0: S_0 > P_0. You bought an option which pays off S_T - P_T as long as St > Pt though the time 0 < t < T. What would be the price of such option ?

Assume you have two stocks S and P so that at initial time t = 0: S_0 > P_0. You bought an option which pays off S_T - P_T as long as St > Pt though the time 0 < t < T. What would be the price of such option ?

*I am looking for a non-arbitrage argument avoiding any specific distribution assumptions (log-normal, normal etc) if possible.