# IV (Implied Volatility)

## Basic Points

- Implied volatility tells us what percentage range that the options market is pricing in as a one standard deviation move (68.3% chance) over the next year.
- For example, if IV is 17%, then it has a one standard deviation’s chance (68.3%) of moving 17% either direction in a year.
- Rather than use historical data to calculate a one standard deviation move, which is what realized volatility does, implied volatility calculates the expected percentage range by how relatively expensive options are.
- If long options are in demand and trading at a strong premium, then implied volatility is going to be higher, which means the options market will be pricing in a wider percentage range.

## Intermediate: Expensive vs Overpriced

Volatility traders face the perpetual problem that we can only know if options are expensive but never really know if they are overpriced, since that would require advanced knowledge of future realized volatility, which is impossible to know beyond the limitations of forecasts and estimates.

The terms ‘overpriced and underpriced’ are not really used by theoretical option traders much anymore, because their usage implies that one knows what the option *should *be worth. In the modern vernacular, one would say that the options are trading with a “high implied volatility” or a “low implied volatility,” meaning that one has some sense of where implied volatility has been in the past, and the current measure is thus high or low in comparison. (McMillan, 2012, p. 689)

One of the ways that this relative expensiveness of IV is gauged on the fly is with IV Rank or IV Percentile, which is available from some brokers and free web resources.

Another major aspect of strategy with IV (and judging whether it is overpriced or not) is how it is highly mean reverting. The IV of longer-duration options is easier to predict for purposes of trading, since there is a strong chance of them returning to deep historical averages, but the margin of error is smaller when predicting changes in IV. This is because longer-duration options have more vega, which as a reminder is a first-order Greek measuring how sensitive the price of an option is to changes in IV.

## Advanced: Greek Dynamics

Implied volatility is of principal importance to option traders because it will shift sometimes very unpredictably based on overall responses by the options market, and being on the right side of that can mean fast money.

The other major Greeks (delta, gamma, and theta) all move predictably and mechanically based on changes in spot, time, and IV. However, vega (changes in IV relative to changes in the price) is by itself is the wildcard where the market is often the most inefficient. This is because theoretical pricing models for options assume that volatility is constant. Meanwhile, volatility is *almost never* constant. This is partly why implied volatility is so inefficient, and interesting to us as traders, since where there is inefficiency there is edge.

## Expert: How IV Is Calculated

Regarding the computation of implied volatility to try and gauge the market’s expectation of future volatility by examining prevailing option prices (Schwager, 2008, p. 579), there is no known closed-form solution for calculating implied volatility. Instead, “implied volatility is the volatility number that, if plugged into a theoretical pricing model along with all of the other inputs, would yield a theoretical value of an option equal to the market price of the same option” (Cottle, 2008, p. 382). What this means is that the process of calculating IV is done with plug-and-play methods that loop in different volatility inputs until there is a match with the listed price. This also assumes that all other inputs–besides volatility–are both known and accurate (Natenberg, 2015, p. 545).

One of many challenges for the options market (when it comes to pricing in efficient IV values) is how realized volatility (RV) bends reliably depending on the time of day. In *Trading Volatility*, Bennett breaks down these repeated patterns for the cash sessions:

For most markets, intraday volatility is greatest just after the open (as results are often announced around the open) and just before the close (performance is often based upon closing prices). Intraday volatility tends to sag in the middle of the day due to the combination of a lack of announcements and reduced volumes/liquidity owing to lunch breaks. For this reason, using an estimate of volatility more frequent than daily tends to be very noisy. Traders who wish to take into account intraday prices should instead use an advanced volatility measure. (2014, p. 236)

This is one of many reasons why the party never stops when evaluating fair IV prices.