Changes in implied volatility are an artifact of the tool (ie the model day count) you use to measure it.

• If you use a calendar day model, you will see IV mechanically increase after a weekend. Wouldn’t it be nice to normalize for this so we can see if IV changed net of this effect?
• The same goes for business day models, but the effect is in the opposite direction.

The fact that one convention undershoots the IV and one overshoots is a giant clue to how we can imply much cleaner IVs that are more stable to the undeniable passage of time.

• Business day models pretend no time has elapsed over a weekend because they presume all the annual volatility is conveniently filed in business days. We know that’s not true.
  • News can come out over a weekend and a Monday price gap doesn’t just belong to Monday — it’s really the sum of what may have invisibly happened to prices over the weekend (if a nuclear bomb dropped in NYC on Saturday you would happily sell your SPY shares 3% under the prior Friday’s close if you could. The price has changed even if the SPY shares can’t print until Monday am).

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• Calendar day models don’t distinguish between quiet periods like weekends or holidays vs busy trading days.

In short…variance does not transpire uniformly. Option models embed an assumption of how time passes. Calendar models assume uniform time passage, business day models assume a lumpy time passage.

The truth is in-between. A model that inches closer to that truth will yield less variation in the implied volatility it spits out as an artifact of how it accrues for the passage of time.

This is the idea of variance time. We acknowledge that time passes over a weekend but variance time doesn’t pass as evenly as clock time. It slows down for a weekend. But it doesn’t slow to zero in the way a business day model assumes.

The solution is to assign weights to different types of days to construct a new ruler that is neither 365 calendar days or 251 business days.

Next Section: Why Use Variance Time