Realized Volatility and Implied Volatility:
Similarities and Differences

In all discussions pertaining to the various forms of volatility trading, be they hedging, speculation, or investing, we must be careful to distinguish between the two most commonly recognized varieties of volatility: actual — often referred to as historical, realized, market, or stock volatility — and implied, which is derived from the prices of options. We shall discuss briefly how each form of volatility is calculated, and then explore some of the most obvious similarities and differences between the two.

Realized Volatility Calculation

There are a few ways in which to determine realized, market, or actual volatility. The RealVol daily formula adopted by The Volatility Exchange uses a traditional standard deviation calculation, assuming a mean of zero for the return of the underlying asset. For example, the daily return of an average stock, or stock index, is slightly lower than one-twentieth of one percent (0.05%), so using a mean of zero has little effect on the ultimate volatility value obtained by the formula, while it greatly facilitates the calculation. Please see our various volatility graphs and volatility charts for a further appreciation of the one-month, three-month, and one-year historical volatilities of a wide variety of underlying assets.

To date, there has not been an exchange-traded realized-volatility futures contract. RealVol futures, options, and futures-like instruments settling to the realized volatility of an underlying, will bridge this gap and provide the world's investment community with the first such listed products.

Implied Volatility Calculation: Implied Volatility Explained

It is interesting to note that, unlike the case for realized volatility, there is no straightforward formula for actually calculating implied volatility. We don’t really calculate implied volatility as much as we observe option volatility, or a volatility index, such as VIX, designed to represent the implied volatility of an array of options. Since a volatility estimate is required as one of the inputs into the Black-Scholes option-pricing model (for options on stocks) or the Black Model (for options on futures), if, instead, we suppose that the observable market price of the option is an input, we “trick” the options model into furnishing the option volatility assumption that was used to price the option in the first place. In essence, we obtain the option's implied volatility by running the option model “backwards.”

So, the best answer to the question, “What is implied volatility?” is: the volatility that one would have to input into the options pricing model in order to arrive at the current option price.

Comparisons and Contrasts

It is an observable phenomenon that, for the most part, the implied volatility surface for a wide range of options on a specific underlying asset averages to a value that is somewhat higher (sometimes significantly so) than the typical volatility that the asset eventually displays (the realized volatility). One explanation for this implied volatility/realized volatility “premium,” or gap, is that sellers of naked options bear an open-ended, unlimited risk and, therefore, command from the buyers, whose risk is predetermined and limited, some form of extra compensation.

Indeed, as RealVol futures trade, it is interesting to note how their pricing reflects such a premium, and how that premium varies over time as one enters and moves through the RealVol calculation period (CP) (see our Glossary). Many of the fascinating studies catalogued in our Volatility Links and Volatility Library sections address the issue of historical implied volatility and its relationship to actual asset volatility.

The Variability of Volatility Itself

Whether implied or realized, there is a stochastic, or random, component to volatility. “Stochastic volatility” refers to the tendency for volatility to fluctuate over time. Indeed, this “volatility of volatility” (“vol of vol”) can be quite pronounced and often furnishes traders of implied volatility options with ample opportunities for profit. In similar fashion, it is expected that the one-month RealVol futures (1VOL), whose annualized realized volatility can be very large, often ranging between 80%–100%, will provide potential investors and speculators with the ability to trade a vehicle that exhibits almost unprecedented levels of variability itself.

Finally, one must also appreciate the similarity that exists between RealVol futures and over-the-counter (OTC) volatility swaps. Volatility swaps and the closely related product variance swaps enjoy considerable popularity, but their access is often closed to the broad trading public. RealVol futures will provide the opportunity for many to experience the benefits of volatility swaps in a listed, easily accessible, but hitherto unavailable, environment.