# Market risk FRTB: calculation of Vega risk charge

I recently started working on a project that requires me to deal with the new market risk standard issued by the Basel Committe: https://www.bis.org/bcbs/publ/d457_faq.pdf

I am trying to calculate the vega risk charge for an equity option that expires in 1.5 months. The idea behind is to apply 1bps point shock to the implied vol. surface on specific tenors, divide the delta PV by 1bps and multiply the result by the implied vol on the shocked tenor.

Following the instructions:

'The equity vega risk factors are the implied volatilities of options that reference the equity spot prices as underlyings as defined along one dimension, the maturity of the option. This is defined as the implied volatility of the option as mapped to one or several of the following maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.'

and further: The assignment of risk factors to the specified tenors should be performed by linear interpolation or a method that is most consistent with the pricing functions used by the independent risk control function of a bank to report market risks or P&L to senior management.

However, expiring in 1.5 months the option should not have sensitivity on the 0.5 year tenor right? How should i interpolate in this case?

Thanks very much for all those that can provide any help. Chris

• Are you reading the Standardised Model (not IMM). If so the the sensitivity has to be fully mapped to one of the specified tenors. In which case it would be 0.5Y.
– Attack68
Nov 18 '19 at 19:00

My reading of it is this:

### Sensitivity definitions for vega risk

21.25 The option-level vega risk sensitivity to a given risk factor[8] is measured by multiplying vega by the implied volatility of the option as follows, where:

(1) vega,$$\frac{\partial V_i}{\partial \sigma_i}$$, is defined as the change in the market value of the option $$V_i$$ as a result of a small amount of change to the implied volatility $$\sigma_i$$; and

(2) the instrument’s vega and implied volatility used in the calculation of vega sensitivities must be sourced from pricing models used by the independent risk control unit of the bank: $$s_k = vega × implied vol$$

Footnote [8]: As specified in the vega risk factor definitions in [MAR21.8] to [MAR21.14], the implied volatility of the option must be mapped to one or more maturity tenors.

This equity option's vega sensitivity is calculated according to its 1.5month matrurity using the bank calculation system but it is mapped to the 0.5Y bucket.

If you had, for example, a short position in a 4month maturity option then that sensitivity could be netted against the 1.5month via the 0.5Y bucket.

• Thank you very much for this. What is still not entirely clear to me is the 'mapping' to the 6 months bucket. Which tenor should i shock (apply the 1 bps absolute shock) on the vol. surface? Should i shock the 1 and 2 months and allocate the weighted sensitivities to the 6 months bucket? Nov 18 '19 at 20:33
• Also, using RiskMetrics I can shock different section of the vol say 25 Delta, 50 Delta and 75 Delta. Which one should i use? Sorry for asking all these (maybe stupid) questions but I cannot find any guidance on this. Nov 18 '19 at 20:41
• The standardised model is simple and conservative in terms of its assessment. Any expiry between 0 and 6mths has a calculation (the banks own) to determine the Vega risk to its own expiry and then that sensitivity is classed or "mapped" as a 0.5y expiry along with others to be netted for latter calculations.
– Attack68
Nov 18 '19 at 22:02
• Thanks very much for your explanation!! I finally understood how this works!! I might come back with other questions on the SA though 😀 Nov 19 '19 at 7:18
• Here I am asking again for help. I have a plain vanilla equity option expiring in 1.8 months (out of the money put) my vola surface have three moneyness level 25delta, 50delta and 75delta and available tenors are in days 30, 60, 91, 122, 152, 182, 273 etc.. the way I would do it is: I check my option delta and shock the closest delta bucket for tenors 30 and 60 days. I would then interpolate the values to find the correct one for 1.8 months. I would then multiply this sensitivity with the implied vol for six months. Would this be correct? Nov 28 '19 at 7:42