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A new method is proposed to obtain the risk neutral probability of shareprices without stochastic calculus and price modeling, via an embedding of theprice return modeling problem in Le Cam's statistical experiments framework.Strategies-probabilities $P_{t_0,n}$ and $P_{T,n}$ are thus determined andused, respectively,for the trader selling the share's European call option attime $t_0$ and for the buyer who may exercise it in the future, at $T; \ n$increases with the number of share's transactions in $[t_0,T].$ When thetransaction times are dense in $[t_0,T]$ it is shown, with mild conditions,that under each of these probabilities $\log \frac{S_T}{S_{t_0}}$ hasinfinitely divisible distribution and in particular normal distribution for"calm" share; $S_t$ is the share's price at time $t.$ The price of the share'scall is the limit of the expected values of the call's payoff under thetranslated $P_{t_0,n}.$ It coincides for "calm" share prices with theBlack-Scholes-Merton formula with variance not necessarily proportional to$(T-t_0),$ thus confirming formula's universal validity without modelassumptions. Additional results clarify volatility's role in the transactionand the behaviors of the trader and the buyer. Traders may use the pricingformulae after estimation of the unknown parameters.

A new method to obtain risk neutral probability, without stochastic  calculus and price modeling, confirms the universal validity of  Black-Scholes-Merton formula and volatility's role