<aside> 📔 A recap of what we know thus far:

• The day-count (I’ve been interchangeably using the word “tenor”) of the option model we use affects the implied volatility we measure.
• Calendar and business-day models are naive in opposite ways.
  • Calendar-day models ascribe an equal amount of variance to every day regardless of whether the market is open or not.
  • Business-day models ascribe zero weight to weekends and holidays — but to be sure, the true price of an asset can change over the weekend even if the change is not observable until the market re-opens.
• We can assign our own weights to days to specify a custom variance day calendar. This is useful because:
  • The implied volatility generated by such a calendar is closer to reality because it deals with how time passes more accurately. Going forward we will call this the “clean” volatility. The implied volatility generated by a naive off-the-shelf 365-day or 251-day model will be called the “dirty” volatility.
  • Clean implied vols are useful because we can compare IVs across expiration schedules (if you trade cross-asset this is critical) more confidently because we are using an implied vol that has less artifacts from a naive computation of “time remaining”. </aside>

I’ve used repetition to make help you keep your mental luggage intact on this journey. My experience, even with other professionals, is this topic puts people’s brains in a blender. If you are following easily, take some pride in that. If not, that’s baseline. Your recourse is to keep re-reading and build a simple calendar mimicking what I did in Excel. All the steps are trivial even if the concept hurts a bit.

This question is a good litmus test for how well you are following:

Where can you observe this clean volatility number?

You don’t observe it directly because the vendor you are using is not deploying an option calculator that assumes a 279.5-day or any other custom day-count year.

But there’s good news…

You can generate it from any implied volatility reading you pull from your current choice of software. We call this process “cleaning” the volatility and it’s actually very simple.

We’ll start with an example, then generalize the method.

Before we do that, we’ll pause to have a closer look at “time remaining”

Variance Time Until Expiry

Recall this schedule (I re-shuffled the columns so you focus on “Time Remaining In Years”):

We are looking at trade dates in January for an option that expires on Dec 31st. We can see that all 3 models disagree about the time remaining.

Most off-the-shelf pricing models assume the 365-day calendar. Let’s add a couple of columns that compute the difference in time remaining from the 365-day model for each of the business day model and the variance day model (recall that our clean model assigns non-business days .25 weight):