Implied Volatility

Why this matters

Strike, Expiration, and Premium listed the things that move an option's price, and all but one can be looked up: the share price, the strike, the date, the interest rate, the dividend. The exception is how much the share is going to move, which nobody knows. Whatever the market collectively guesses is built into every premium, and it can be read back out. That number, implied volatility, is the closest thing the options market has to a price tag. Someone who buys an option without looking at it is buying something without asking what it costs.

Two kinds of volatility

Volatility is a measure of how widely a share's price fluctuates, and it comes in two kinds.¹

• Historical volatility, also called statistical volatility, measures actual price changes over a past period. It's usually stated as the annualized standard deviation of the share's daily price changes, the measure from Distributions, Standard Deviation, and Fat Tails.
• Implied volatility is a measure of how much the marketplace expects the price to move, based on the price of the option. It's the volatility the market implies.

One looks back and can be calculated from a price history. The other looks forward and can only be inferred. Implied volatility has no direct connection to past volatility. It's a measure of predicted future movement, and the market is the final judge of its level.²

Reading it out of a price

A pricing model such as Black-Scholes takes five inputs: the share price, the strike, the time to expiration, the interest rate, and the volatility.¹ Four are known. If the option's market price is known too, the model can be run backwards to find the one volatility that produces that price.

Volatility put into the model	Call's value
20%	$2.25
30%	$3.25
37%	$3.90
50%	$5.20
70%	$7.15

If the call is trading at $3.90, its implied volatility is 37%. If the same call were trading at $5.20, with the share still at $50, its implied volatility would be 50%. Nothing about STU's price would differ. Only the price of the option would.

This turns implied volatility into a common yardstick. Premiums can't be compared directly across shares, strikes, or dates: $3.90 on a $50 share for three months and $11 on a $300 share for six weeks say nothing side by side. Their implied volatilities can be compared, because each is the same quantity, a yearly percentage. It also means implied volatility moves whenever option prices are pushed around. Increased demand and higher premiums mean higher implied volatility, with no change in the share.²

From a percentage to a range

An implied volatility is an annualized standard deviation. To apply it to a shorter period, multiply by the square root of the fraction of a year.

Expected move over a period ≈ Implied volatility × √(Fraction of a year)

Period	Sum	One standard deviation	Range around $50
One trading day	37% ÷ √252	2.3%	$48.83 to $51.17
One month	37% × √(1 ÷ 12)	10.7%	$44.65 to $55.35
Three months	37% × √(1 ÷ 4)	18.5%	$40.75 to $59.25

If price changes followed a normal distribution, the share would finish inside a one-standard-deviation range about two times in three. Real share prices have fatter tails than that, so large moves come more often than the arithmetic suggests.

The table makes the option chain from earlier lessons readable in a new way. The $55 call needs STU to rise 10% within three months just to reach its strike. At an implied volatility of 37%, that's a move of about half a standard deviation, well within the ordinary range, which is why the call costs $2.00 and not ten cents.

There's a quicker reading too. The at-the-money call and put together, $3.90 + $3.40 = $7.30, cost 14.6% of the share price. That's roughly the size of move, in either direction, that the market is charging for over the three months. A buyer of both needs STU to move more than that to come out ahead.

The rest of this lesson is for members

Still to come in this lesson: Implied volatility is the price, Why it rises before news and falls after, The VIX, How good a forecast is it?, What implied volatility doesn't tell you, the key takeaways, and 2 quiz questions with explanations.

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