On the Practical Point of View of Option Pricing

In this note we describe a new approach to the option pricing problem by introducing the notion of the safe (and acceptable) for the writer price of an option, in contrast to the fair price used in the Black-Scholes model. We study the problem from the practical point of view concerning mainly the over the counter market. This approach is not affected by the number of the underlying assets and is particularly useful for incomplete markets. In the usual Black-Scholes or binomial or some other approaches one assumes that one can invest or borrow at the same risk free rate $r>0$ which is not true in general. Even if this is the case one can immediately observes that this risk free rate is not a universal constant but is different among different people or institutions. So, the fair price of an option is not so much fair! Even worse, concerning all the continuous time models that assumes construction of replicating portfolios, one should reconstruct the portfolio continuously in time! We also define a variant of the usual binomial model trying to give a cheaper safe or acceptable price for the option.