# RealVol Indices Terms

### Realized Volatility

Realized volatility is the “actual volatility,” “statistical volatility,” or “asset volatility” that the underlying has displayed over a specific period. The term “realized volatility” is very closely related to “standard deviation.” Realized volatility is a specific form of standard deviation. If one were to use daily returns of an underlying (instead of actual prices) and annualize the results, standard deviation becomes realized volatility. VolX uses a modified version of the standard deviation formula. We will refer to the RealVol version of realized volatility as “realized volatility,” “realized vol,” or simply “vol.”

### Measurement Not Observation

One of the key issues regarding realized volatility is that it is measured not observed. In other words, one cannot look at a particular price and determine what volatility that represents. The only way to calculate realized volatility is to get prices over time and then use a realized volatility formula to calculate the movement of prices for that time frame. This is a key concept because all realized volatility formulas must use historical prices in order to calculate a result.

For example, if the evening news reports that the price of gold is currently \$1,000 per ounce, it has expressed only the price of gold. The current price says nothing about how much gold had to move to get to \$1,000. Did it just move down from \$2,000? Or, did it just move up from \$999? One cannot tell unless previous (historical) data are also used. Thus, saying that the price of gold is now \$1,000 tells us nothing about its volatility, because we lack a historical perspective.

### Implied Volatility

There is another type of volatility known as “implied volatility.” Implied volatility is based on the relative expensiveness of associated options premiums. Implied volatility is a completely different approach to expressing volatility and often differs in value from realized volatility. The intricacies of implied volatility are beyond the scope of this document; hence, when we use the term “volatility,” we are referring to realized volatility.

### Underlying

The “underlying” can be just about anything that has a daily price. For example, the underlying can be a physical asset, security, futures contract, index, currency, bond, swap, measurement, etc.

### Underlying Reference Price

We will use the term Underlying Reference Price (URP) to refer to the actual daily closing price that the underlying  has displayed, or will go on to display. The URP is the “closing,” “final,” or “settlement” price for the day. The URP is an especially attractive value for calculating Realized Volatility because of its ease of use, transparency, and wide dissemination to market participants. Roughly speaking, therefore, the underlying is the “asset,” while the URP is the “closing price.”

However, there are two exceptions: The first is when there is a market disruption event. In such a case, one needs to follow the rules on Market Disruption Events detailed later in this document. The second is when calculating the RealVol Real- Time Index. VolX will use  the most recent underlying price throughout the trading day (“Today”) as the URP, even though the market may not have closed.  Such an exception occurs on today’s value only and not for any other day in the past.

### Defined Days

As noted, there are three time frames for RealVol Indices: 21 trading days, 63 trading days, and 252 trading days. However, because of the potential for a market disruption event (MDE) where the market never opens and hence never closes, the actual number of trading days may be less than expected. When this occurs, the number of actual trading days (“trading days”) will be less than the expected days (“Defined Days”). Note: We cannot count a non-trading day’s volatility as zero just because a market disruption event eliminates an entire day of trading.

For further clarification: weekends are not trading days; holidays are not trading days; a regularly scheduled trading day is a “trading day.” However, a trading day where the market and all of its surrogate markets do not open, and hence cannot close, causes the number of trading days to be less than the number of Defined Days for purposes of the RealVol Index calculation.