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Choosing the Time Fraction for Implied Volatility Near Expiry

Article Quant Q&A · Author: Xerium
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Summary

The document raises a practical convention question for implied volatility calculations when an option expires within hours. It contrasts calendar year scaling, using 365 days, with a trading year convention using 252 days, then asks how to scale a fraction of a day for an option with six hours remaining. One proposed approach apportions the calendar day by 24 hours; the other apportions a trading day by seven trading hours.

No answer or pricing comparison is included, so the document does not establish which convention is appropriate or calculate an implied volatility. The choice depends on the option market’s time convention and the intended treatment of nontrading hours, holidays, and the exact expiry timestamp. The question highlights that a small remaining time can make the annualization convention consequential, but offers no evidence about how a specific venue or model handles it.

Key ideas

  • Implied volatility calculations require a time to expiry expressed in year units.
  • Calendar day and trading day conventions use different annual time scales.
  • For an intraday expiry, the remaining hours must be converted using a consistent convention.
  • The document poses the convention question but does not provide a resolution or calculation.

Tags

OptionsVolatilityDerivatives pricing
Full text
# What $T$ to use a few hours till expiry when calculating implied volatility?


# What $T$ to use a few hours till expiry when calculating implied volatility?












I am trying to calculate the implied volatility given an option price that is a few hours till expiry. The issue I am having is that I am not sure if it's better to use $T=\frac{1}{365}$ (case 1) or $T=\frac{1}{252}$ (case 2) for the daily increment. Then for the hour increment if an option that is 6 hours till expiry, if it's case 1, would we then use: $$T=\frac{1}{365}\frac{6}{24}$$

Or then if it's case 2:

$$T=\frac{1}{252}\frac{6}{7}$$ (If there is 7 hours of trading)

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.