IVOL — Inferred Volatility Stat
IVOL stat is a volatility value that can be inferred from the market price of a RealVol futures and its PVOL stat (partial volatility stat). 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 root-mean-square formula (perhaps more than once) to the PVOL 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 RealVol futures. Many traders would compare implied volatility to inferred volatility to judge the relative expensiveness between options and RealVol futures, respectively.
Inferred Vol within the RealVol Calculation Period
Once the calculation period (CP) begins,
each night's close brings another data point to the RealVol daily formula,
and, ultimately, to the calculation of the expiration settlement
of RealVol futures. The returns already logged
furnish a PVOL, which contributes to part of the RealVol futures'
current price.
However, other than at the expiration itself, at any point during
the CP, a RealVol 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 RealVol 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 CP
of a September 1VOL have passed, and that PVOL is 25.00. Nine
trading days remain to expiration, and the current price of the
RealVol 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:
RVFP = RealVol futures price (current market)
WP = the fractional weight attributed to the partial-volatility
(PVOL) period
PVOL = Partial realized volatility
WI = 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 CP, RealVol intends
to disseminate IVOLs as a
further aid to traders of RealVol futures. Options traders, in particular,
may want to compare these IVOLs to the implied volatilities of
options whose maturities match that of the RealVol futures, 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 RealVol futures
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 RealVol futures.
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 CP
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 RealVol futures, even before the start
of that contract's CP, and for which, therefore, no PVOL is yet
available. The following serves as an illustration of such a calculation.
Suppose, for simplicity, that RealVol futures 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 CP of a 3VOL that expires
on March 31. In addition, the next quarterly 3VOL, which expires
on June 30, and whose CP 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 RealVol futures
prices. Market participants can watch the spread between implied
volatility and inferred volatility for additional trading opportunities.
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