Reducing Implied Volatility Average Noise with Consistent Weights
Summary
The document considers daily averages of option implied volatilities when the available contracts change over time because options expire or data are missing. A raw daily average can move simply because its constituents changed. Carrying the previous average forward using average returns may reduce that effect, but can drift away from the current market level.
The proposed solution is to define a weighting scheme and compute a weighted statistic each period, allowing the weights to change over time. As an illustration of the design principle, the answer describes a broker’s constant maturity, constant moneyness volatility measure: it selects options near the market across two expiries, fits volatility by strike, interpolates variance to a target maturity, and derives a summary volatility. This example shows how explicit rules for maturity and moneyness can make a changing option set more comparable. The document does not prescribe universal weights; the appropriate construction depends on the metric’s intended meaning and the available data, so the resulting series remains a designed summary rather than a uniquely correct market average.
Key ideas
- Changing option constituents can create jumps in a daily implied volatility average even when the surviving options are unchanged.
- A weighted average can use period-specific weights to define which observations contribute and how much.
- A constant maturity and moneyness measure aims to improve comparability as options expire.
- The weighting and selection rules should reflect the metric being measured; no universal scheme is specified.
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Full text
# How do you avoid noise in daily averages?
# How do you avoid noise in daily averages?
Let's say I am computing daily implied volatilities of a range of options and averaging them.
On any given day, the range of options I have available may be different from the range of options I had the day before. This could be due to options expiring but also simply due to lack of data availability.
If I compute my averages on day $t$ and day $t + 1$ by just averaging the implied volatilities, then that might give some noise simply caused by the fact that e.g an option I had on day $t$ expired on day $t + 1$, but all other options had the exact same volatility. So perhaps I should instead set my $t + 1$ average equal to my $t$-average scaled up by the average return on day $t+1$.
... but then over time, my averages and the actual average on the market risk getting completely out of sync.
So what to do about this conundrum? I either just compute the averages every day and accept the noise, or I average the returns and risk getting very much out of sync with the actual average.
What is the best way to solve this?
## Answer by krkeane (score 3)
https://quant.stackexchange.com/a/80477
You need to define a weighting scheme that you can use for each period. Weighted statistics are straight forward to compute. Your weights can change for each time $t$. For example, $$ \begin{aligned} wx_t &= \sum\limits_{i=1}^N \left(w_{i,t} x_{i,t}\right) \\ ~\\ w_t &= \sum\limits_{i=1}^N \left(w_{i,t}\right) \\ ~&\\ \bar{x}_t &= \frac{wx_t}{w_t} \end{aligned} $$ One broker (IBKR) provides customers results from the following calculation:
> 30-day (V30) Implied Volatilities Implied volatility is calculated using a 100-step binary tree for American style options, and a Black-Scholes model for European style options. Interest rates are calculated using the settlement prices from the day’s Eurodollar futures contracts, and dividends are based on historical payouts. The 30-day volatility is the at-market volatility estimated for a maturity thirty calendar days forward of the current trading day. It is based on option prices from two consecutive expiration months. The first expiration month is that which has at least eight calendar days to run. The implied volatility is estimated for the eight options on the four closest to market strikes in each expiry. The implied volatilities are fit to a parabola as a function of the strike price for each expiry. The at-the-market implied volatility for an expiry is then taken to be the value of the fit parabola at the expected future price for the expiry. A linear interpolation (or extrapolation, as required) of the 30-day variance based on the squares of the at-market volatilities is performed. V30 is then the square root of the estimated variance. If there is no first expiration month with less than sixty calendar days to run, we do not calculate a V30.
The intent of this IBKR computation is construction of a constant maturity, constant moneyness summary of implied volatility for an underlying financial instrument.
You need to similarly define your metric of interest.
> All models are wrong but some are useful. George BoxShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.