What We Know And What We Don´t Know

The price of an option should depend on several factors: Spot asset price, Strike level, Time to maturity, Interest rates, Volatility, Expected asset return, Liquidity concerns, Crash-o-phobia, Supply-demand disequilibriums, Upcoming elections, Artificial mark-ups by dealers trying to sink a counterpart, Etc, etc (anything deemed relevant by buyers and sellers).

In this list there are items that we know and items that we don´t know. Obviously, we only know a few. But the others are also important and should count. Of course, we can´t develop a model that includes a parameter for every single relevant factor (if only because these tend to change with time). Ideally, we would want a model that provides parameters for each of the known factors, plus an additional single parameter that acts as catch-all where dealers can dump at once all the other unknown factors. Black-Scholes wonderfully offers such service. The catch-all parameter is dubbed “implied volatility”, but it should be clear that the unknown volatility factor does not monopolize the catch-all. So many considerations go into that number that it would be unfair to define it by a single one of them. Thus, the price of an option is made up of stuff that we know and stuff that we don´t know. Of stuff that we know and something called implied volatility, not stuff that we know and volatility.

People say that implied volatility is the “market expected volatility”. It´s much more than that. Do not let volatility elbow out all the other unknown parameters and unfairly monopolize the ever-important figure of implied volatility.