Distributional divergence, statistical experiments and consequences in option pricing

Abstract

Distributional Divergence and Statistical Experiments are used herein for a positive stochastic process. This framework provides, under mild assumptions, Risk Neutral Probability (-ies) P* for a stock price process which does not have necessarily either to satisfy a Stochastic Differential Equation or to follow a model, both non-realistic assumptions. The results contribute in understanding the relation between P*, statistical contiguity and market's informational efficiency. P*-price of European option is obtained, confirming the universal quote of the Black–Scholes–Merton price for the class of calm stock prices that includes log-normal price. Other consequences are presented.