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.