Reporting of specific information concerning template C106.01: “Instrument 23”

Our issue and its corresponding question rely on the manner we should report a specific information concerning the template C106.01 “SBM.Risk sensitivities by Instrument” – 2022 benchmarking exercise – based on a constraint of this template regarding the number of lines we can report. That is: “Institutions shall report each combination of Instrument number, Risk identifier (column 0010), Bucket (column 0020) and Additional identifier (column 0030) only once.” Our doubt is linked to the “instrument 23” and to the new benchmarking sensitivities’ template submission. Concretely, we have received a validation due to a negative volatility we reported within the template. The reason is that “instrument 23” Collar component is based on two transactions: a 7.5% Cap and a 2.5% Floor. The Vega Net sensitivity of both transactions (therefore, the Collar Vega sensitivity) is positive, even though one of the transaction’s Vega is positive while the other one is negative. Since the Collar figures must be reported only with one “line”, it forces us to reach a negative Collar FRTB-SA weighted Vega value with the multiplication of a positive Collar Vega sensitivity and a positive “average” volatility, which mathematically speaking is not possible.

Please, let us use the following “dummy” figures as an example of the situation for a single risk factor to ease the understanding: Cap transaction Vega sensitivity 0.5_0.5 = -7 Floor transaction Vega sensitivity 0.5_0.5 = 10 Equivalent Collar Vega sensitivity 0.5_0.5 = (-7) + 10 = 3   Additionally, the implied volatility used to evaluate each transaction is positive. Let us use as an example the following figures: Cap transaction Vega volatility 0.5_0.5 = 2% Floor transaction Vega volatility 0.5_0.5 = 1% Therefore, the FRTB-SA weighted Vega value is negative. Following the previous example: Cap transaction weighted Vega value 0.5_0.5 = -7 * 2% = -0.14 Floor transaction weighted Vega value 0.5_0.5 = 10 * 1% = 0.1 Equivalent Collar Vega weighted Vega value 0.5_0.5= (– 0.14) + 0.1 = -0.04 Finally, the resulting equivalent Vega volatility value results negative. Collar Equivalent Vega volatility 0.5_0.5 = -1.33%