Here’s a stylized example:

• It’s December 1st, 2023 and a straddle expires on Friday, December 29th, the last day of the year.
• Assume your 365-day off-the-shelf model shows a 20% implied vol for the entire month. In other words, the price of the straddle over the course of the month decays exactly at its Black-Scholes prescribed theta and always imputes 20%.

Do you believe that the market’s consensus for implied volatility is actually unchanged?

I would argue that the implied vol is actually changing.

Let’s look at the measurements to start:

You can see the clean vol is moving around because the cleaning ratio is changing. The relative proportion of days til expiry is not static as each calendar day rolls off because the clean model assigns different weights to business and non-business days.

The 365-day model shows constant vol but we can see the sawtooth pattern in the clean vol.

Why?