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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 youenter image description here

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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

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  • $\begingroup$ 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 $\endgroup$ – HJA24 Jun 4 '19 at 10:16
  • $\begingroup$ Yes, It should be based on remaining maturity, not the original maturity, $\endgroup$ – Magic is in the chain Jun 4 '19 at 11:28
  • $\begingroup$ 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? $\endgroup$ – HJA24 Jun 4 '19 at 12:24
  • $\begingroup$ 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 $\endgroup$ – HJA24 Jun 5 '19 at 7:31
  • $\begingroup$ 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. $\endgroup$ – Magic is in the chain Jun 5 '19 at 16:20

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