Essentially, all models are wrong, but some are useful.
—George Box, in “Robustness in the Strategy of Scientific Model Building.” In R. L. Launer and G. N. Wilkinson, eds., Robustness in Statistics. New York: Academic Press, 1979.
Option pricing involves reasonably complex mathematics. How deeply does a trader need to delve into this? To answer this we need to understand what a model does. What is a model?
A model is a map. It simplifies the world, keeping the detail we need and excluding the rest. It is not meant to be a perfect representation of reality. The only way a map can be perfect is if it is the same size as the world. Then we have gained nothing.
Options are complex. Their prices are dependent on a number of variables and the prices change very quickly. Add to this the fact that one underlying may have hundreds of options associated with it and that these all have relationships to each other, and having a model to make things simpler seems clearly advantageous. That is not to say a model is essential. Many retail option traders, and even some professionals, trade without one, either using options as leveraged directional instruments or to implement the static strategies we look at in Chapter 6.
But a model, used intelligently, greatly simplifies things. It expresses the fast moving option prices as functions of more slowly evolving parameters. It also enables us to compare options of different strikes, maturities and underlyings in a simple ...