Distribution assumption
Now that I have pointed out the shortcomings of the normal distribution assumption in quantifying price change distributions, I intend to develop an option pricing model based on this very assumption. There is method in such an apparently contradictory approach. Knowing the limitations of a theoretical model in advance may allow us to correct its deficiencies after the fact using empirical information extracted from real price data. This pragmatic approach, I submit, is quite different from the conventional theoretical approach to option pricing which revolves around a mathematically perfect formula not applicable in the real world.
There are other benefits from proceeding initially on the normal assumption. Perhaps most important, the reader will be able to directly compare the simplified option pricing model I’m going to develop from first principles with the “million dollar formula” that dominates options literature. Before attemping to construct this model, I would like to make a few observations on price distributions in general and discuss ways of expressing these distributions as succinctly as possible.