Volatility Is Not Volatility

Few concepts in the financial markets are more talked-about than so-called implied volatility. Implied volatility essentially tells us what number (given a certain option price) traders are inputting under the volatility parameter that goes into the pricing model.

An implied volatility figure of, say, 30 per cent means the average consensus input for the volatility parameter that was entered by traders was 30 per cent. In other words, to reach the desired consensus price for the option, the volatility input has to be exactly 30 per cent.

Implied volatility is an important measure for several key reasons, but not for the reason that is most often cited. Most people take it as an article of faith that implied volatility represents the market's forecast of future realised volatility (ie, true expected market turbulence). If three-month implied volatility is 30 per cent then surely this must mean that traders are expecting the next quarter to be a wild ride, so would go the conventional wisdom.

Unfortunately, implied volatility is not a mirror into forthcoming turbulence. While the implied volatility number would contain traders' view on future real volatility, this is only one of its ingredients. Implied volatility is about much more.

Just like a sausage-making machine, the implied volatility number is fed with a bunch of different (and many times entirely unfamiliar) ingredients. To confuse implied volatility with the market volatility forecast would be akin to confusing the whole with one of its parts. Flatly stated, an implied volatility of 30 per cent does not mean an expectation of 30 per cent realised volatility. Implied volatility is, in fact, a liar.

Why the deceit? Blame it on Black and Scholes. When using this most popular of option pricing models (in fact, the place from where implied volatilities are quoted) traders input figures under volatility that do not stand (exclusively) for volatility. They do so to obtain conveniently the option price that they want. When deciding on the volatility number that would deliver the desired result traders obviously consider their expectations as to future turbulence, but would consider other things at the same time. Traders' opinions concerning any issue that can affect the price of an option would be included in the implied volatility number.

In effect, then, implied volatility is best redefined as the conduit through which traders obtain the prices that are deemed optimal, a catch-all where they correct for all those relevant aspects not rightly captured by the model's machinery. Real expected volatility will always be a key component of implied volatility, possibly the most important one, but it will never account for the whole picture. When it comes to option pricing, "volatility" does not always stand for volatility.

Thus, a higher implied volatility number does not automatically imply that traders are expecting higher market turbulence. A high level of implied volatility might imply the perception of high future real volatility, but it likely also reflects a host of other factors. Liquidity concerns, crash-o-phobia on the part of traders, and particular supply-demand disequilibriums all can result in bumped-up implied volatility numbers. Implied volatility is also many times inflated as a way to correct for the known deficiencies in the probabilistic assumptions behind Black-Scholes, which unrealistically assigns little chance to extreme market movements taking place.

Any unseemly factor could alter implied volatility. For instance, during the famed Long Term Capital Management episode of late 1998, equity options counterparts to the fund reportedly marked the volatility parameter up by a lot, as a way to protect their interests. A naive observer might have looked at the 40 per cent figure and concluded "the market is surely forecasting a wild ride".

Most academic studies on the subject have focused on trying to answer whether implied volatility is a reliable predictor of realised volatility. Those analyses are a bit like comparing apples with oranges. The truly interesting insight would be to explain what part of implied volatility is forecast volatility and what is "other stuff", and what exactly that stuff is. Only then could we discover the true market expectation for trouble on the horizon.

ptriana@profesor.ie.edu