Volatile Irrelevance
And yet, the argument could be made that Black-Scholes makes volatility irrelevant. Heretical as this might sound, Black-Scholes may have produced volatility-independent option pricing. Thanks to the Nobel-caliber model, traders can price options without taking volatility into account, if they so wish. There is no need to develop a view as to future market turbulence. The desired option price can be obtained even if no volatility estimate is taken into consideration.
Of course, the Black-Scholes model does include a parameter named “volatility” that is supposed to stand for, well, volatility. That was the very intention of Fisher Black and Myron Scholes when they developed the model. You can´t price an option without inputting some number under the volatility parameter. However, that does not mean that that number stands for expected real future volatility. That number may simply be a conduit used by traders to arrive at the desired optimal option price, the ingredient necessary to churn out exactly the correct outcome from the pricing sausage machine. For all we know, no actual volatility forecast may be embedded into that number. Who is to guarantee that traders are even expressing a view on future turbulence when inputting a number under volatility?.
In theory, of course, volatility should affect the value of an option. Generally speaking, the more expected turbulence the merrier for the owner of options. But this is only theory. In practice, option prices are determined entirely by human action, not theoretical truth. We assume that humans take future volatility into account when pricing options, but we just don´t know for sure. Perhaps the biggest advantage of the Black-Scholes model is that one can get desired prices without having to develop a view on future realized volatility (just like the model does not force you to develop a view as to the expected return of the underlying asset).
Another reason to argue that expected volatility may be irrelevant to traders is that their concerns lie entirely with implied volatility (the number consensually inputted under “volatility” by the market), as they live or die by the mark-to-market of their books, and this is of course determined by changes in implied volatility (essentially, traders´ opinions). Unlike many on the “buy side”, which usually keep the option until maturity and thus care about future volatility (due to the need to develop a view as to whether the contract would end up in-the-money), dealers are judged (and compensated) exclusively by the market value of the position.
Implied volatility and expected realized volatility are simply not the same thing (the existence of the volatility smile, among other things, very clearly tells us so). While the latter may be embedded into the former, it is just one of the component parts. Blunty stated, implied volatility is a bunch of stuff. A catch-all that allows traders to make relevant all the crucial aspects that the pricing model does not take into account, things like liquidity concerns, crash-o-phobia on the part of traders, demand-supply disequilibriums and in general anything that is deemed practically relevant when it comes to pricing an option. Traders love Black-Scholes precisely because it allows them to easily and conveniently make such corrections. The known deficiencies in the Black-Scholes machinery thus result in the paradox that when it comes to option pricing, volatility is not volatility.
If implied volatility is all that matters to a trader, what´s left for poor neglected real volatility?. Even if we assume that expected turbulence is a part of implied volatility (ie, that traders do in fact develop a view as to future realized volatility when pricing the option), this probably wouldn´t help much. Unless one can develop a view on future implied volatiltiy as a whole, just being able to forecast one of its components won´t help traders develop a sense as to their future mark-to-market exposure. But getting implied volatility right is bound to be challenging. It is one thing to forecast real market turbulence or the expectation of it (parameters that could be reasonably calculated to a certain degree), and another thing to predict other traders´ opinions about a whole bunch of stuff (real volatility but also anything else that would affect their gut feelings).
Should traders then lose much sleep over future real volatility? Maybe not.
ptriana@profesor.ie.edu
