Minimum Capital Requirements for Market Risk

For each risk class, to calculate curvature risk capital requirements a bank must apply an upward shock and a downward shock to each prescribed risk factor and calculate the incremental loss for instruments sensitive to that risk factor above that already captured by the delta risk capital requirement using the following step- by-step approach: (1) For each instrument sensitive to curvature risk factor k, an upward shock and a downward shock must be applied to k. The size of shock (ie risk weight) is set out in [7.98] and [7.99] . (a) For example for GIRR, all tenors of all the risk free interest rate curves within a given currency (eg three-month Euribor, six-month Euribor, one year Euribor, etc for the euro) must be shifted upward applying the risk weight as set out in [7.99] . The resulting potential loss for each instrument, after the deduction of the delta risk positions, is the outcome of the upward scenario. The same approach must be followed on a downward scenario. (b) If the price of an instrument depends on several risk factors, the curvature risk must be determined separately for each risk factor. (2) The net curvature risk capital requirement, determined by the values CVR and CVR for a bank’s portfolio for risk factor k described in above [7.5] (1) is calculated by the formula below. It calculates the aggregate incremental loss beyond the delta capital requirement for the prescribed shocks, where (a) i is an instrument subject to curvature risks associated with risk factor k; (b) x k is the current level of risk factor k; (c) V i (X k ) is the price of instrument i at the current level of risk factor k; (d) V i (X k (RW (curvature)+) ) and V i (X k (RW (curvature)-) ) denote the price of instrument i after x k is shifted (ie “shocked”) upward and downward respectively; (e) (curvature) is the risk weight for curvature risk factor k for instrument i ; and (f) Sik is the delta sensitivity of instrument i with respect to the delta risk factor that corresponds to curvature risk factor k, where: (i) For the FX and equity risk classes, S ik is the delta sensitivity of instrument i; and (iii) For the GIRR, CSR and commodity risk classes, S ik is the sum of delta sensitivities to all tenors of the relevant curve of instrument i with respect to curvature risk factor k. (3) Within bucket aggregation: the curvature risk exposure must be aggregated within each bucket using the corresponding prescribed correlation ρkɭ as set out in the following formula, where: (a) The bucket level capital requirement (K b ) is determined as the greater of the capital requirement under the upward scenario ( ) and the capital requirement under the downward scenario ( Kb ). Notably, the selection of upward and downward scenarios is not necessarily the same across the high, medium and low correlations scenarios specified in [7.6]. (i) Where K b = K , this shall be termed “selecting the upward scenario”. (ii) Where K b = K b , this shall be termed “selecting the downward scenario”. (iii) In the specific case where K = Kb if ∑ k CVR >∑ k CVR , it is deemed that the upward scenario is selected; otherwise the downward scenario is selected. (b) Ψ( CVR k , CVR ɭ ) takes the value 0 if CVR k and CVR ɭ both have negative signs and the value 1 otherwise. (4) Across bucket aggregation: curvature risk positions must then be aggregated across buckets within each risk class, using the corresponding prescribed correlations γ bc , where: (a) S b = ∑ k CVR for all risk factors in bucket b, when the upward scenario has been selected for bucket b in above (3)(a). S b = ∑ k CVR otherwise; and (b) (S b , S c ) takes the value 0 if Sb and S c both have negative signs and 1 otherwise. The delta used for the calculation of the curvature risk capital requirement should be the same as that used for calculating the delta risk capital requirement. The assumptions that are used for the calculation of the delta (ie sticky delta for normal or log-normal volatilities) should also be used for calculating the shifted or shocked price of the instrument. [7.17] states that banks must determine each delta sensitivity, vega sensitivity and curvature scenario based on instrument prices or pricing models that an independent risk control unit within a bank uses to report market risks or actual profits and losses to senior management. Banks should use zero rate or market rate sensitivities consistent with the pricing models referenced in that paragraph. Calculation of aggregate sensitivities-based method capital requirement