If you annualize volatility with 252 days can you use that number in a 365-day option model?
a thorough answer to a reader
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Friends,
A Moontower reader asked a question that gets into one of the most confusing topics for option traders:
If I'm pricing options using calendar days(365), then I should even annualize realised volatility by multiplying 18.8(√256) instead of 16 (√256, approx trading days). In order to compare the VRP ratio on same scale, am I right?
I know firsthand from watching people wrestle with option models that this topic has put many brains in a blender. It's worth a blog-post sized answer. My hope is that you will not only walk away clear-headed but bursting with ideas to explore.
A typical starting point
You compute close-to-close realized daily volatility for the past 252 trading days. Those days comprise the past year. You get an average daily vol of 1.875%. You annualize it by multiplying 16 to get 30% volatility.
observations:
Before the addition of Juneteenth, a non-leap-year had 252 trading days.
After Juneteenth was added to the holiday calendar, there are 251 trading days.
A leap year will typically have 1 more trading day than a non-leap year.
2024 is a leap year that has 366 days and 252 trading days which is what we expect for a leap year.
If the daily standard deviation is 1.875% you should annualize by multiplying by √252 but traders will typically just estimate by multiplying by 16 (ie √256). If you are building a model, don’t use the estimate, but a lot of trader workflow involves quick assessments so it’s worth noting where the mental math shortcuts are.
The central question is:
Can you put 30% annual volatility into a typical 365-day option model or should you have annualized by √365?
The answer is a satisfying mix of reasoning and arithmetic.
