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As we have seen, it is possible to calculate the value of a european style option if the probability distribution for all the possible underlying values at expiration is known.

If this distribution were exactly known, no simplification in terms of using a model would have to made: the calculation of an option premium would be based a calculation based on facts.

It is therefore easy to understand that the most important problem for option pricing is to find an acceptable prediction method for these probability distributions.

The Black and Scholes model uses a method for the description of the underlying price movements commonly known as the random walk theory.