Implied Volatility for a Stock

Question

I'm looking for Python libraries or formulas to compute Implied Volatility (IV) for a stock. Most of the web searches indicate that IV is related to an option contract.

Can you explain if and how implied volatility for a stock is computed, and how it is different from the implied volatility for an option contract.

My client is looking at the screen below from "Options Alpha" and he wants me, as a developer, to compute that number. We've been using PolygonIO, and they have IV for an option contract, but not for a stock by itself. I'm trying to determine first, if it is a logical request, then secondly how to go about it.

I also found this page on OptionsAlpha site, but still trying to make sense out of it: https://optionalpha.com/podcast/understand-how-implied-volatility-works

But the screen shot below does not reference any options contract, it seems to have an IV per the stock.

Instructions like this that tell you how to compute IV always seem to reference an option contract: https://www.wallstreetmojo.com/implied-volatility-formula/

This looks promising - using "Average True Range": https://www.youtube.com/watch?v=KJgvIlBJeYg

Answer 1

There's not a single "implied volatility" for a stock. Implied volatility by definition is the volatility implied by option prices. It's computed by taking an option pricing model (commonly the Black-Scholes model) and trying different volatilities until the prices matches what's seen in the market. It's very common for options at different strikes and maturities to have different implied volatilities. Options close to expiry tend to have higher implied volatilities, but whether that's based on fundamentals or traders willing to pay a little extra for near-term options is up for debate.

As far as what that site is reporting, it's anyone's guess. Most likely it's the "at-the-money" IV for the options with strikes that are closest to the current stock price, or some weighted average of the two closest strikes. You could take a few examples and try and reverse-engineer what the site is doing, but there's no consensus on the implied volatility of a stock outside of using option prices.