Inferred Volatility

Inferred Volatility ("IVOL") is defined as any calculation of the remaining Realized Volatility to expiration, as forecast by traders of one or more VolContract futures. It is the volatility that can be inferred by applying a root-mean-square formula (perhaps more than once) to a partial realized volatility ("PVOL") and the current market price, or prices, of one or more VolContract futures.

Inferred Vol Within the Realized-Volatility Period

Once the Realized-Volatility Period ("RVP") begins, each night's close brings another data point to the VolX Formula, and, ultimately, to the calculation of the expiration settlement ("EVOL") of VolContract futures. The returns already logged furnish a PVOL, which contributes to part of the VolContract futures' current price.

However, other than at the expiration itself, at any point during the RVP, a VolContract futures' value depends not only on the PVOL but also on traders' perception of the realized volatility remaining to be displayed by the underlying asset. Indeed, once we know the PVOL and the current market price of the VolContract futures, we may infer the traders' estimate of remaining volatility by a straightforward mathematical formula.

Suppose, for example, that 12 trading days of the 21-day RVP of a September 1Vol have passed, and that PVOL is 25.00. Nine trading days remain to expiration, and the current price of the VolContract futures is, say, 27.00. What estimate of realized volatility for the remaining nine trading days may we infer from that price? Application of the so-called root-mean-square formula tells us that the correct answer is 29.46.

In essence, if IVOL is the estimate of remaining realized volatility, we solve the following formula for IVOL:

Where:
VC = VolContract futures current market price
W_P = the fractional weight attributed to the partial-volatility (PVOL) period
PVOL = Partial Realized Volatility
W_I = the fractional weight attributed to the inferred-volatility (IVOL) period
IVOL = Inferred Volatility

Substitution of the values into the formula yields:

Solving, we obtain IVOL = 29.46.

In addition to providing PVOLs throughout the RVP, VolX intends to disseminate IVOLs, or inferred realized volatilities, as a further aid to traders of VolContracts. Options traders, in particular, may want to compare these IVOLs to the implied volatilities of options whose maturities match that of the VolContract, as spread opportunities might arise. For example, suppose IVOL is 29.50 and at-the-money (ATM) options implied volatilities are, say, 32.00. We might consider a trade wherein we buy the VolContract and sell an ATM straddle. We then delta-neutral hedge the straddle, to expiration. We might, therefore, capture all, or part, of the differential between the 32.00 implied volatility of the options and the 29.50 inferred volatility of the VolContract.

Note: The resulting volatility captured via delta-neutral hedging of an options position may differ from the volatility realized by the underlying for many reasons including, but not limited to, the actual path of the underlying price movement, the precise execution prices for any follow-up trades, and transaction costs. One should understand all of the risks before implementing such a trading strategy.

Inferred Vol Outside of the RVP

Finally, although a somewhat more involved calculation, it is possible to infer a realized volatility for any remaining time period to the expiration of a VolContract, even before the start of that contract's RVP, and for which, therefore, no PVOL is yet available. The following serves as an illustration of such a calculation.

Suppose, for simplicity, that VolContracts expire on the last calendar day of the month. Suppose, as well, that it is February 1, and that we are one month into the RVP of a 3Vol that expires on March 31. In addition, the next quarterly 3Vol, which expires on June 30, and whose RVP begins on April 1, is also listed and currently trading. Prices are as follows: PVOL of the March 3Vol: 20.00; current market price of the March 3Vol: 22.00; and current market price of the June 3Vol: 24.00. What IVOL may we deduce for the period beginning on the current date (February 1) until the expiration (June 30) of the June 3Vol? The following series of calculations may be used to derive the answer.

First, applying the same technique as utilized earlier, we determine the IVOL of the March 3Vol, for the February 1-March 31 period. The root-mean-square formula yields 22.93 for the IVOL of this March contract.

Next, we observe that the current market price of the June 3Vol is 24.00, and that this price reflects the realized-volatility forecast for the period of April 1-June 30. A weighted value of the aforementioned 22.93 IVOL, for February 1-March 31, and the 24.00 forecast, for the period of April 1-June 30, is now obtained from a second application of the root-mean-square formula.

Where:
IVOL = Inferred Vol for the period of February 1-June 30
W₁ = the fractional weight attributed to the first inferred-volatility period
IVOL₁ = Inferred Volatility of the March 3Vol
W₂ = the fractional weight attributed to the second inferred-volatility period
IVOL₂ =Inferred Volatility of the June 3Vol (equals the current price)

The resulting IVOL, which can be interpreted as the Inferred Vol for the period of February 1-June 30, is 23.58.

In conclusion, one can deduce implied volatility from options prices, and one can also get an inferred volatility from VolContract prices. Market participants can watch the spread between implied volatility and inferred volatility for additional trading opportunities.