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?
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.