# Volatility

## Basic Points

- When we say volatility in trading, we usually mean either implied volatility (IV) (the expected percentage move over the next year based on
*option prices*with 68.3% confidence) or realized volatility (RV) (the expected percentage move over a period of time based on*historical prices*with 68.3% confidence). - Volatility-sensitive trades have the extra dimension of not only being right about price, but also being right about how quickly price can move (or not move) compared to what the market is pricing in.
- Also, the slang “vol” is usually considered a reference to IV, especially as “event vol”. For clarity, it is usually helpful to specify explicitly whether we mean IV or RV.

## Advanced: Types of Volatility

There are various different kinds of volatility in math or nature, but options pricing ended up sticking with volatility that is defined based on standard deviation, despite some glaring inefficiencies. The good news for us as traders is that whenever there are market inefficiencies, there are always edges (competitive trading advantages) to discover. Volatility has consistently remained what is arguably the most inefficient aspect of the market.

As an example of using a different type of volatility to help forecast or measure implied volatility, we can track ATR (average true range) which is simply the average rolling range including the gaps (such as overnight jumps). ATR shows how range-based volatility is changing on a simple moving average, and might give us clues for how wide we expect the range to be. However, this is different from the type of volatility used by the options market which is based on standard deviation. To forecast option implied volatility directly, it is common to use RV forecasts in order to estimate what IV should look like in the near future, such as with GARCH models.

## Expert: Understanding Volatility

A single standard deviation is what is estimated to have about a 68.3% chance of happening, but it can be easier to think of that as approximately 2/3. If the options market is pricing in that there is a 2/3 chance it will move at least 30% (in either direction), then the directional volatility trader has the challenge of how there is only about a 1/3 chance of that being priced in if picking only one direction. This is the attraction to more neutral option strategies that focus on trading IV, such as iron condors or iron butterflies. Rather than only have an estimated 1/3 chance of hitting a one standard deviation move on one specific side, the volatility trade gets to tap into the average of that 2/3 chance if betting on it to stay in that range. But then this can come with its own kind of tail risk (an unexpected but catastrophic outcome) which becomes attractive to counterparties.

To drill down a bit more into what volatility is, as Natenberg frames it in *Option Volatility & Pricing, “*In a sense, volatility is a measure of the speed of the market” (Natenberg, 2015, p. 69). What this means is that stock traders only buy and sell the spot underlying for a profit, but for options traders it matters how fast the spot underlying moves in comparison to how much the options market is betting for the spot underlying to move over a certain period of time.

What it means for standard deviation to be the input for a theoretical options pricing model is that “the volatility we feed into a pricing model represents a one standard deviation price change, in percent, over a one-year period” (p. 77). Although volatility is tailored for the standard deviation 52 weeks out, an expected move can be approximated for a day if dividing IV by 16, or it can be approximated for a week if dividing by 7.2. And then that expected move, representing a standard deviation for that time period, is additive (p. 75). What this means is that, for example, a standard deviation of 4 entails that 2 standard deviations would be 8, and three standard deviations would be 12.

Another set of main properties of volatility is how it is strongly mean reverting and how it is proportional to the square root of time. It is not that difficult to predict over long periods of time that volatility will revert to deep historical averages. However, to balance this, traders have the extra challenge of how the margin for error is smaller for trading IV on longer timeframes because longer-dated options have more vega, and this increases the penalty for mispricing volatility. “Depending on the time to expiration, the effect of a two or three percentage point volatility error on a long-term option may be greater than a five or six percentage point volatility error on a short-term option” (p. 391).

Regarding volatility’s relationship to time, volatility is the square root of variance which itself is proportional to time; it follows that volatility is proportional to the square root of time. This relationship with time is how we can calculate the [implied] expected move on any timeframe, and also explains how the rate of time decay (theta) is proportional to volatility, with the value that IV contributes to an option’s price disappearing as time approaches zero.