5. Volatility

Historical Volatility

Volatility calculation based on past values based on the changes of each day and getting the variance
Historical volatility is usually shown in the year period
It is taken from stock prices

Realized Volatility

The realized volatility measures what actually happened in the past, in the option price
It is a past measurement, it is not a calculation based on past values, but just what the volatility actually was in a given period of time

Implied Volatility

It in an annualized percentage point
Taken from options prices
It allows to make a determination of just how volatile the market will be going forward
Implied volatility comes from the price of an option and represents its volatility in the future
It represents one standard deviation range of price moves in 1 year, meaning that it encompasses the entire range of all the possible price moves from -implied volatility to +implied volatility

So, 68 percent of the time (because of the normal distribution), the price of an asset in a year will be in the range of Price - (Price * IV) to Price + (Price * IV)

If we want to express the IV in a time range other than a year, the formula would be

Price Range = Price ± (Price * IV * √time)

Where time is expressed as a fraction or multiple of 1 year

Price Range = Price ± ( Price * IV * √(days/365) )

Example with these values

Stock price: 100$
Implied Volatility: 30%
Time: 180 Days
The expected 1 standard deviation move would be

± 100 * .30 * √(180/365) = ±21.06$

More Accurate Version the price range from implied volatility

This version assumes that the distribution of prices is not normally distributed, but it has a lognormal distribution . A log-normal distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. In this case it means that the return of the changes in the asset price is a normal distribution, but the price itself is distributed log-normally, because it cannot go lower than 0
So It does not represent one standard deviation price move in 1 year, it represents one standard deviation range of return in 1 year

Price Range = Price * e^[ (r - (IV*IV)/2)*t ± IV*√t ]

This formula is used when using large time frames or the implied volatility is very large, generally the normal distribution formula is more used

IV Rank

IV Rank is the at-the-money (ATM) average implied volatility relative to the highest and lowest values over the past 1-year
For example, if implied volatility ranged between 30% and 60% during the last 52 weeks in hypothetical stock XYZ, and implied volatility is currently trading at 45%, XYZ would have an IV Rank of 50
Succesptible to being skewed to spikes

IVR = (Current IV - 1 Year IV Low) / (1 Year IV HIgh - 1 Year IV Low)

IV Percentile

Similar to implied volatility rank, implied volatility percentile provides insight into the current level of implied volatility as compared to the last 52 weeks of data
The metric reports the percentage of days over the last 52 weeks that implied volatility traded below the current level of implied volatility
For example, if IV percentile in XYZ is 90%, that would mean that the current IV is higher than 90% of all previous IV measurements in one year

VIX

Widely followed index representing the IV for the S&P600 Index over the next 30 days, expressed in annualized form
The VIX cannot be bought directly, instead, it can be traded thought ETF, options and futures