ABSTRACT
Distributional Divergence and Statistical Experiments are used herein for a positive stochastic process. This framework provides, under mild assumptions, Risk Neutral Probability (-ies) 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 statistical contiguity and market's informational efficiency. -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.
Acknowledgments
Many thanks are due, in particular to Professor Alexander Meister, Editor, and a referee for the prompt processing of the paper and the encouragement. Very special thanks are due to Professor Wolfgang K. Härdle for his continuous encouragement concerning this work. Many thanks are also due to the Department of Statistics and Applied Probability, National University of Singapore, for the warm hospitality during my summer visits when most of the results were obtained.
Disclosure statement
No potential conflict of interest was reported by the author(s).