Stock prices will rarely follow the assumed model but, when stock's transaction times are dense in the interval $[t_0,T),$ they determine risk neutral probability (-ies) ${\cal P}^*$ for the stock price at time $T.$ The remaining available risk neutral probabilities at $T$ correspond to stock prices with different jumps-variability. The findings indicate that ${\cal P}^*$ may be a mixture. The necessary and suficient condition used to obtain ${\cal P}^*$ is related with the flow of information and concepts in Market Manipulation; it contributes in understanding the relation between market informational efficiency and the arbitrage-free option pricing methodology. ${\cal P}^*$-price $C$ for the stock's European call option expiring at $T$ is also obtained. For "calm" stock prices, $C$ coincides with the Black-Scholes-Merton price and confirms its universal validity without stock price modeling assumptions. Additional results for calm stock: a) show that volatility's role is fundamental in the call's transaction, b) clarify the behaviors of the trader and the call's buyer and c) confirm quantitatively that the buyer's price carries an exponentially increasing volatility premium.
