Skip to content
All library documents

Constructing Covariance-Bucket Vega from Forward Volatility

Article Quant Q&A · Author: HJA24
Read the original

Summary

The note explains how to estimate relationships between option volatility buckets for a covariance-based view of portfolio vega. It proposes dividing maturities into intervals and using at-the-money implied volatility, with each later interval represented by forward volatility derived from total variance at the interval boundaries. For example, the variance accumulated to a longer maturity is decomposed into variance through the earlier maturity plus variance over the forward interval.

To estimate dependence, form daily log changes in the volatility series and calculate correlations across buckets. This method preserves the distinction between volatility exposures at different horizons instead of treating all option vegas as interchangeable. The answer gives a construction and estimation procedure, but does not settle questions about bucket overlap or provide empirical validation. Results will depend on the maturity points, volatility data, and historical sample used.

Key ideas

  • Use at-the-money implied volatility as the basis for volatility buckets.
  • Derive forward volatility from the difference in total variance across maturities.
  • Estimate cross-bucket dependence by correlating daily log changes in volatility series.
  • The estimated covariance structure depends on bucket definitions and historical data choices.

Tags

OptionsVolatilityStatisticsRisk management
Full text
# Understanding methodology behind the covariance bucket vega


# Understanding methodology behind the covariance bucket vega












I am reading "Dynamic Hedging" from Mr. Taleb. I understand that you cannot simply aggregate all the vegas of your option portfolio and classify this as the portfolio's vega. So, now I want to reconstruct the covariance bucket vega. Basically, I divide the option universe into different maturities and bucket them. The first step is to create a correlation matrix between the different buckets. The book states "the operator builds a correlation matrix of the percentage moves between forward-forwards buckets, say by slicing time into 0-30, 30-60, ...., and so on. Using historical analysis, the operator then fills in the correlations between the relative periods."

Question: So, what is exactly the measure unit of this procedure? The ATM-IV of each bucket? And is this overlapping or non-overlapping? Please help me understand. Thank you

## Answer by Magic is in the chain (score 1, accepted)

https://quant.stackexchange.com/a/45879

Yes looks like ATM volatility. It’s forward (he also calls it forward forward volatility). Say you have the volatility of an option with 30 days maturity, $\sigma_1$ and $T_1$; and the volatility of an option with 60 days maturity, $\sigma_2$ and $T_2$.The 0-30 bucket will have $\sigma_1$ , whereas the 30-60 days bucket will have the forward volatility between 1 and 2, $\sigma_{12}$ which you may calculate, for example, from the following:

$\sigma_{2}^2 T_2=\sigma_1^2 T_1+\sigma_{12}^2\left(T_2-T_1\right)$

And so on for the other maturities.

You can then calculate the log difference of each series daily values, e.g., $\ln \sigma_1(t)-\ln \sigma_2(t-1)$, where the t in bracket represents a trading day, and then calculate the correlation between these series

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.