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

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

• Thanks for your reply. I have a dataset that consist of weeklies, two-weeklies, monthlies, quarterlies and half-yearly options. At some point the weekly has the same days to maturity as the half-yearly option. Should I both include them in the 0-7d bucket? Or is each optionserie its own bucket, no matter the days until maturity? So 0-7, 7-14, 14-30, 30-90 and 90-180. Thanks Jun 4 '19 at 10:16
• Yes, It should be based on remaining maturity, not the original maturity, Jun 4 '19 at 11:28
• Okay, but what should I do if the both the weekly and the half-yearly option has less than 7 days until maturity. I include them both in the 0-7d bucket. But then? I take both ATM IVs and get the average of the log differences of each serie within that bucket? Jun 4 '19 at 12:24
• And what is the procedure if there is no forward vol for a particular bucket during a trading day? I have a limited amount of expirations, so sometimes there is no data Jun 5 '19 at 7:31
• Re-first, instead of averaging I would pick one representative based on liquidity and/or resemblance to the positions. And same goes for missing, find a reasonable proxy. Jun 5 '19 at 16:20