What Does Implied Volatility Really Mean?
In Know Your Options, I tend to mention Implied Volatility quite often. I’m sure most readers already understand the general idea that options with high IVs are expensive and options with low IVs are cheap.
Here at Zacks, we’re currently working on the development of some advanced options tools that we hope will make options analysis and trading easier and more profitable – just like our existing tools do for equities, ETFs and mutual funds.
Our goal is to make the interfaces as intuitive as possible, including on-screen definitions and examples of all the functionality so that you can just open it up and start using it – no lengthy manual required.
While preparing some of those on-screen support tools, it occurred to me that I’ve never definitively explained Implied Volatility from a mathematical standpoint and that it might be interesting.
So here it is:
Volatility measures the rate at which a security moves up and down. If a security is moving up and down quickly, volatility will be high. Conversely, if a security is moving up or down slowly, volatility will be low.
Implied volatility is a measure of what the options markets think volatility will be over a given period of time (until the option’s expiration), while historical volatility (also known as realized volatility) is a recording of how the underlying actually moved over a specified past period.
Generally, option traders look to buy options when implied volatility is low since premiums are lower, in hopes of seeing the underlying stock move in a favorable direction along with an increase in volatility which will make premiums increase. And traders look to write options when implied volatility is high as option premiums tend to be higher, in hopes of seeing the underlying stock move in a favorable direction to his/her position along with a decrease in volatility which would make premiums decrease.
The number you see represented as “Implied Volatility” is expressed as a percentage. Black-Scholes and other related options pricing models assume that future returns on an underlying asset can be represented by a normal distribution (bell curve.)
(Technically, it’s actually a lognormal distribution, but the slight difference isn’t important for these examples.)
An implied volatility of 20% means the options market estimates that a one-standard deviation return in the underlying (positive or negative) over the course of the next year will be 20% of the current price. (One standard deviation includes roughly 2/3 of instances in a (log)normal distribution, with the remaining 1/3 of returns lying outside that range.)
To determine the expected one-standard deviation move for options with a period of time remaining that's different than exactly one year, divide the implied volatility by the square root of the number of those periods in a year.
An option has one day remaining and an implied volatility of 20%.
There are about 256 trading days in a year. The square root of 256 is 16.
20% / 16 = 1.25%
The options markets expect that a one standard deviation move over the remaining (one day) life of the option is 1.25%. That means that 2/3 of the time the return on the underlying will be distributed within 1.25% of the current price and 1/3 of the time the return will lie outside this range.
If instead there were 64 days remaining until expiration:
There are 4 64-day periods in a trading year. The square root of 4 is 2.
20% / 2 = 10%
A one-standard deviation expected return over the 64-day life of the option is 10%.
Supply and Demand
Implied volatility is also often seen as a measure of supply and demand for options. Like securities prices, implied volatilities rise when there is more buying interest and fall when that interest fades or there is selling interest. Because most traders do not intend to hold options all the way to expiration, high (or rising) implied volatilities can therefore be interpreted as an indication of increased demand for those options and low implied volatilities an indication of reduced demand.
Now I’d like to ask for your help. In general terms, was this subject too simple, just about right or over your head? I want to tailor both the content in Know Your Options and the functionality in our new analysis suite to the intended audience - you.
Please feel free to drop me a line at firstname.lastname@example.org and let me know. Thanks!
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