Glossary of Terms, Abbreviations, and Symbols
VolX^{}
Exchange
The Volatility Exchange: The “doing business as” (DBA) name of The VolX Group Corporation.
VolX: The abbreviation for The Volatility Exchange.
RealVol Products
RealVol: The name used for all products from VolX that relate to, or base their values on, realized volatility. RealVol Products can be divided into categories: RealVol Instruments, RealVol Indices, RealVol Stats, and RealVol Formulas. Within each category are the specific RealVol Products. RealVol Instruments include: RealVol Futures, RealVol Options, RealVol Futures Options, and RealVol Swaps. RealVol Indices include: VOL, VOV, DVOL, VCOR, VAR, RVOL, and HVOL. RealVol Stats include PVOL, TVOL, and IVOL. RealVol Formulas include: RealVol Daily Formula and RealVol RealTime Formula among others.
RealVol Instruments: Tradable financial instruments that settle to the 1month (21 day) RealVol Index known as VOL
RealVol Indices: The family of daily and realtime indices that base their values on realized volatility as defined by the RealVol Formulas.
RealVol Formulas: The daily and realtime formulas that base their values on realized volatility as defined by VolX.
vol: The generic term for volatility.
vol of vol: The generic term for the volatility of volatility.
RealVol
Instruments
RealVol Futures: Futures contracts that ultimately settle, or expire, to the appropriate VOL index.
VOL: The abbreviation/symbol for RealVol Futures.
RealVol Options: Option contracts that ultimately settle, or expire, to the appropriate VOL index. RealVol Options could also include option contracts that ultimately settle, or expire, to the associated RealVol Instrument (e.g., RealVol Options expiring to RealVol Swaps).
VOLS: The symbol for RealVol SPY Options, soon to be traded on the BOX Exchange.
RealVol Swaps: Standardized, centrally cleared, exchangetraded or overthecounter (OTC) swaps that ultimately settle, or expire, to the appropriate VOL index.
Anticipatory Period: The first of two distinct periods over the life of a RealVol Instrument. It begins on the first day that a RealVol Instrument is listed for trading and ends on the last trading day before the start of the calculation period. Note: Not all RealVol Instruments have an anticipatory period. If the listing date coincides with the start of the calculation period, then the RealVol Instrument enters immediately into the second of the two distinct periods — the calculation period.
AP: The abbreviation for the anticipatory period.
Calculation Period: The second of two distinct periods over the life of a RealVol Instrument, and the period used by the corresponding VOL index to determine the expiration value. (Note: the ending dates of the calculation periods of individual RealVol Instruments will correspond to the associated options expiration schedule of the underlying asset or instrument.)
CP: The abbreviation for the calculation period.
RealVol Indices
Use RealVol Indices for insight into the realized volatility of an underlying.
RealVol RealTime Index: There is only one realtime index in the RealVol suite of
risk indices. The RealVol RealTime Index (VOL) uses a
timeweighted, intraday underlying price to provide a
realtime, 21day, realized volatility.
For instance, if the time today is 75% of the way through the current trading day, then weight the partial day's return by 75% (this partial return is selfweighting) and weight the full day's return from 22 days prior by 25% (this term needs to be specifically weighted). All other days are fullweight, fullday (closetoclose) returns. In this manner, the index encompasses 22 data points but the weight of exactly 21 trading days at any moment throughout the trading day.
Such a realtime update can be useful as a guide to
position entry or exit within the trading day or for very
shortterm daytraders in the underlying.
RealVol Daily Indices: All other RealVol Indices are daily. This means that they are updated only once each trading day and are based only on daily observations of the underlying. In addition, all RealVol Daily Indices come in six time frames: 1day, 1week (5 trading days), 1month (21 trading days), 1quarter (63 trading days), ), 1halfyear (126 trading days), and 1year (252 trading days). The six time frames correspond to the investment horizon of most traders. For periods longer than one year, realized volatility deviates little from its very longterm average so is generally estimated to be a constant.
VOL Indices
The realized volatility indices (VOL) measure the interday (closetoclose) realized volatility of an underlying using the RealVol Daily and RealTime Formula. As discussed, there are five time frames for all indices including VOL. The special flagship VOL Index is based on the 1month time frame only. The reason for flagship status is that the 1month version is the only one used for tradable instruments.
VOV Indices
Realized volatility of realized volatility indices (VOV) measure the realized volatility of VOL using the RealVol Daily Formula a second time on the same data. Trading instruments on realized volatility compels one to discover the risk of those instruments. To do so, one needs to calculate the vol of vol. (Note: The second iteration through the data is always performed on a 1month (21day) basis, regardless of the time frame of VOL.)
DVOL Indices
The full day, overnight/intraday realized volatility indices (DVOL) measure the realized volatility based on the previous day’s close and today’s open, high, and low data of an underlying using the RealVol Overnight/Intraday Formula. One can think of DVOL as another measure of 24hour price risk of an underlying using additional data points for greater accuracy.
VCOR Indices
Correlation indices (VCOR) measure the correlation between the underlying and its VOL. They are calculated by using the RealVol Correlation Formula. Use VCOR for insight into the linear relationship between the underlying and its realized volatility. (Note: Two time frames, the 1day and 1week correlations, will not be calculated.)
VAR Indices
Realized variance indices (VAR) measure the interday realized variance of an underlying using the RealVar Daily Formula. VAR Indices are simply the square of VOL. One can think of VAR as another measure of interday price risk of an underlying. Variances are easier to sum, average, and combine because the result is linear as opposed to that of volatility, which is a curve function.
RVOL Indices
The Rough Vol model (Rough Fractional Stochastic Volatility or “RFSV”) forecasts realized volatility. According to the model, created by Professor James Gatheral of Baruch College, the log of daily high/low realized volatilities is well approximated by fractional Brownian motion with a Hurst parameter H close to zero. VolX uses the Rough Vol model to create the RVOL indices, which forecast the VOL index over six standardized time frames. Our preliminary research has shown that the Rough Vol model approximates future realized volatility more accurately than the options market (implied volatility) and certain GARCH models. Both the HARK (see below) and Rough Vol models have similar longrun predictive accuracy, but arrive at their forecasts in quite different manners — often diverging significantly over short periods of time.
HVOL Indices
HARK (Heterogeneous AutoRegressive model cast into a Kalman filter framework) is a forecast of realized volatility. It is a dynamic extension of the asymmetric (i.e., with leverage effects) HAR model where the parameters are continuously and optimally updated by the Kalman filter according to the statistical properties of the overnight/intraday realized volatility input (DVOL). This allows flexibility and fast adaptation to the original HAR model, which was created by Professor Fulvio Corsi of Ca' Foscari University of Venice. VolX uses the HARK model to create the HVOL indices, which forecast the VOL index over six standardized time frames. Our preliminary research has shown that the HARK Vol model approximates future realized volatility more accurately than the market (implied volatility) and certain GARCH models. Both the HARK and Rough (see above) Vol models have similar longrun predictive accuracy, but arrive at their forecasts in quite different manners — often diverging significantly over short periods of time.
RealVol^{} Stats
Use RealVol Stats for insight into the realized volatility of a RealVol instrument.
PVOL: Partial volatility. The todate subset of realized volatility within the CP.
IVOL: Inferred volatility. The volatility that can be inferred from the market price of a RealVol Futures (or its synthetic equivalent using option combos; i.e., long call/short put or long put/short call) and the associated PVOL. The concept is similar to the notion of implied volatility. Implied volatility is the relative expensiveness of an option’s premium as calculated via an options pricing model and solving for the volatility input. Similarly, inferred volatility is the relative expensiveness of a RealVol Futures price obtained by applying a rootmeansquare formula (perhaps more than once) to the PVOL stat and the current RealVol Futures price. The result is the aggregate of traders’ forecasts (including perhaps a risk premium) of the remaining realized volatility until expiration of the underlying asset. Many traders would compare implied volatility to inferred volatility to judge the relative expensiveness between options and RealVol Futures, respectively.
TVOL: Theoretical volatility. Any calculation of a theoretical value of a RealVol Futures contract based on associated options prices using the Heston Model and a rootmeansquare formula.
RealVol^{}
Formulas
Underlying Reference Prices: In regard to the RealVol Daily Formula, the onceperday values used for the inputs to the RealVol Daily Formula. Typically, they will be the daily “closing,” “last,” “final,” or “settlement” prices of the underlying asset, instrument, index, measurement, or other daily value over a defined period. In regard to the RealVol RealTime formula, the current, or realtime, underlying futures price will be used in addition to the daily prices just described.
URP: The abbreviation for Underlying Reference Price(s).
Realized Volatility: The actual or historical volatility that an asset or instrument displays. All realized volatilities at VolX are based on the RealVol Formulas.
RealVol Daily Formula:A mathematical formula used to calculate the annualized standard deviation of continuously compounded daily returns of an underlying asset or instrument, assuming a zero mean, no degrees of freedom, and an annualization factor of 252 trading days regardless of the exact number of trading days in the year. The same formula is applied to three distinct concepts: (1) the general calculation of any realized volatility used by the VolX exchange; (2) the specific calculation of any VOL index or VOV index; and (3) the specific calculation of any PVOL stat.
RealVol RealTime Formula: All of the design elements described for the RealVol Daily Formula are the same for the RealVol RealTime Formula. To convert from a daily to a realtime value, one needs to start with the RealVol Daily Formula, then incorporate the current underlying price (“today’s” price) and a weighting scheme. Doing so provides continuous updates throughout the trading day and delivers to traders a useful, intraday realtime indication of daily realized volatility. At VolX, it was decided to convert only the flagship 1month VOL (also known as VOLm) index to realtime. Essentially, the formula measures an exact 21day realized volatility even while we are within the new, most recent, trading day.


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