Scaling Overnight Volatility to an Intraday Expiry

Summary

The document explains a simple way to estimate volatility for an expiry shorter than the shortest point on a volatility surface. It uses the overnight quote and treats variance as accumulating evenly over the quote’s effective period. To estimate an eight-hour volatility, determine the actual time from the surface’s effective time to the overnight expiry, convert the quoted volatility to variance, scale variance by the ratio of the desired duration to that period, and convert back to volatility.

Under the example’s simplifying assumption that the overnight period is exactly one day, the resulting adjustment is the overnight volatility multiplied by the square root of the fraction of a day represented by eight hours. The effective expiry can vary by market, surface source, and seasonal timing, so the duration should be measured from the relevant timestamps rather than assumed to be exactly twenty-four hours. The method also assumes variance accrues uniformly through the interval and does not account for intraday patterns or event-driven jumps.

Key ideas

• Scale variance in proportion to elapsed time when extrapolating to a shorter expiry.
• Convert volatility to variance before scaling, then take the square root to recover volatility.
• Measure the overnight period from the surface’s effective time to its actual expiry.
• The square-root-of-time adjustment assumes uniform variance accumulation.

Tags

# How to extrapolate shorter tenor from volatility surface?


# How to extrapolate shorter tenor from volatility surface?












Overnight(ON) volatility is the first input of a volatility surface, 1 weeks, 2 weeks and so on... Say I have a volatility surface with ON expiry of 1 day, is there anyway to extrapolate volatility for 8 hours expiry?

## Answer by Ang Yiwei (score 0, accepted)

https://quant.stackexchange.com/a/55621

Volatility surface explains the variance evenly spread across the duration, starting from effective time when it is published.

For 8 hours expiry, referring to ON volatility is enough. Next, calculate the duration by taking the difference of the expiry of ON volatility and the effective time of the surface. For instance a NY surface will be expiring at GMT14 and 15 on Summer/Winter respectively, depending on the source of the surface you received. The duration ideally should be slightly more than a day.

Convert the into volatility into variance by simply squaring it, and multiplying with a ratio of 8 hours to the duration of ON volatility, it will be one-third if we assume ON volatility expires exactly 24 hours. Finally, taking a square root to convert the variance back to volatility.

A direct approach is simply multiplying the ON volatility by square root of 8/24.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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