Treat the life of an option as a series of bets

In discussing the performance of a theoretical pricing model, it is important to remember that all models are probability based.

Even if we assume that we have all the right inputs into the model and that the model itself is correct, there is no guarantee that we will show a profit on any one trade. More often than not, the actual results will deviate, sometimes significantly, from what is predicted by the theoretical pricing model.

It is only over many trades that the results will even out so that, on average, we achieve a result close to that predicted by the theoretical pricing model.

However, option-pricing theory also suggests that for a single option trade there is a method by which we can reduce the variations in outcome so that the actual results will more closely approximate what is predicted by the theoretical pricing model.

By treating the life of an option as a series of bets, rather than one bet, the model can be used to replicate long-term probability theory.


This is one of the many passages and charts I find in books and articles on a daily basis. They span many disciplines, including:

I occasionally add a personal note to them.

The whole collection is available here.