Interpreting the Basel Equity Vega Requirement Along One Dimension

Summary

The document asks how to interpret the Basel framework’s requirement to calculate equity vega “along one dimension.” It considers a two-year option whose theoretical vega depends on strike and maturity, then describes projecting the exposure to adjacent regulatory tenors and summing volatility-weighted contributions. The central uncertainty is whether the strike dimension can be discarded by choosing a conventional volatility, such as the at-the-money point, at each tenor.

No definitive answer or supporting regulatory interpretation is provided. The example is a question about how to treat the volatility surface, including skew and smile, when mapping option sensitivities into regulatory buckets. It therefore illustrates a practical ambiguity in translating a multidimensional market risk exposure into a regulatory measure, but does not establish that an at-the-money-only approach is compliant. Readers would need to consult the relevant Basel text or authoritative supervisory guidance before applying the proposed calculation.

Key ideas

• The question concerns how to map equity option vega under the Basel framework’s one-dimension wording.
• A two-year option’s vega is described as depending on both strike and maturity.
• The example allocates vega to neighboring regulatory tenor buckets and weights contributions by volatility.
• The document does not resolve whether using only at-the-money volatility is the correct regulatory treatment.

Tags

# How to interpret “along one dimension” for Equity Vega under the Basel framework (RBC21.12)?


# How to interpret “along one dimension” for Equity Vega under the Basel framework (RBC21.12)?












I am trying to compute vega under the Basel framework for equity options. When I look at RBC21.12, I see this:

So I wonder if “along one dimension” means that, after calculating the theoretical vega, I should, for instance, just take the ATM volatility differentiated only by the corresponding tenor: 0.5, 1, 3, 5, and 10 years.

Let’s consider a simple example: an equity option maturing in 2 years. I compute the theoretical vega $\nu = \nu(K,T)$, which for simplicity we assume only depends on strike $K$ and maturity $T$.

Based on my understanding, once I get $\nu$, I then project that vega to the maturities 1 and 3 years, so I get:

$$ \nu \;\rightarrow\; (\nu_1, \nu_3). $$

Now, if I take my associated volatility surface and, because it has to be “along one dimension,” I can just pick a single strike by convention (e.g., ATM), then calculate the volatility for 1 and 3 years by interpolation. Hence, the “regulatory vega” would be:

$$ (\sigma_1 \cdot \nu_1,\;\; \sigma_3 \cdot \nu_3)\;\;\rightarrow\;\;\nu_\text{total} = \sigma_1 \cdot \nu_1 \;+\; \sigma_3 \cdot \nu_3. $$

Is this the correct interpretation of “along one dimension” under the Basel standard for equity vega? i.e. simply ignore the strike dimension (thus ignoring skew/smile) and use a single volatility per tenor (like an ATM vol)? Or is there some other approach that should be followed?

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