Skip to content
All library documents

Allocating Two-Day Option Volatility Using Variance

Article Quant Q&A · Author: purr
Read the original

Summary

The document considers how to split a two-day swaption’s annualized volatility into daily volatilities when the two days have different event weights. The proposed setup assigns Thursday twice Friday’s daily volatility, reflecting an assumed higher-movement day, and asks how to obtain the breakeven daily levels from the two-day quote. The original attempt averages volatility linearly, which does not correctly combine independent daily risk contributions.

The response says to add variances rather than volatilities. It gives one equation equating the sum of the two daily variances to twice the squared average daily volatility, and another expressing the assumed two-to-one volatility relationship. Solving these equations yields each day’s volatility. This is a concise allocation method under the stated weighting assumption; the document does not discuss whether the assumed weights are empirically justified or how calendars, correlations, or market conventions might alter the setup.

Key ideas

  • Daily variances, rather than daily volatilities, add when combining the two days.
  • The two-day volatility constraint can be expressed as a sum of squared daily volatilities.
  • An assumed ratio between daily volatilities provides a second equation for solving the allocation.
  • The result depends on the chosen event weighting and the assumptions of the setup.

Tags

OptionsVolatilityDerivatives pricing
Full text
# How to find volatility of a 1 day option based on 2 day annualized volatility


# How to find volatility of a 1 day option based on 2 day annualized volatility












first time -I'm curious as to how the following would work:

I have a 2 day(only includes full day of Thursday and Friday) swaption with a volatility of 100 bps.

We also know the weights we've assigned for the next 2 days, i.e thursday has a weight of 2(we multiply the daily bp vol by 2 - this can be due to a market event causing rates to move - i.e Fed meeting), and Friday is just a standard weight of 1.

How would we go about finding the daily bp vol breakeven for Thursday and Friday.

I tried the following but am uncertain if it is correct, because it may not be a linear interpolation:

100/(sqrt(252) =6.2599 avg daily bp vol

2x + x = 2*(6.299) - multiply by 2 because 2 biz days

x= 4.1966(fridays vol; Annualized: 66.67)

2x = 8.399 (thursdays vol; Annualized: 133.33)

Thanks!

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/73814

That’s pretty close, but you should add the variances not the vols. Thus if the daily vols for Thursday and Fridayvrespectively are $v_1$ and $v_2$, we have the two equations $$v_1^2 + v_2^2= 2*6.2599^2$$ and $$v_1=2v_2$$. These can be solved for $v_1$ and $v_2$.

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.