1.Institutions shall calculate delta general interest rate risk (GIRR) sensitivities as follows:
S_{r_{kt}} = \frac{V_i(r_{kt} + 0.0001, x, y \dots) - V_i(r_{kt}, x, y \dots)}{0.0001}
the sensitivities to risk factors consisting of risk-free rates shall be calculated as follows:
where:
S_{\mathrm{r}_{\mathrm{kt}}} | = | the sensitivities to risk factors consisting of risk-free rates; |
r_{kt} | = | the rate of a risk-free curve k with maturity t; |
V_{i} (.) | = | the pricing function of instrument i; and |
x,y | = | risk factors other than r_{kt} in the pricing function Vi; |
S_{x_{j}} = \frac{\mathrm{V}_{i}(\overline{\mathrm{x}}_{ji} + 0.0001 \overline{\mathrm{I}}_{m}, y, z \dots) - \mathrm{V}_{i}(\overline{\mathrm{x}}_{ji}, y, z \dots)}{0.0001}
the sensitivities to risk factors consisting of inflation risk and cross-currency basis shall be calculated as follows:
where:
S_{\mathbf{x}_j} | = | the sensitivities to risk factors consisting of inflation risk and cross-currency basis; |
\bar{x}_{ji} | = | a vector of m components representing the implied inflation curve or the cross-currency basis curve for a given currency j with m being equal to the number of inflation or cross-currency related variables used in the pricing model of instrument i; |
\overline{\mathrm{I}}_m | = | the unity matrix of dimension (1 × m); |
V_{i} (.) | = | the pricing function of the instrument i; and |
y, z | = | other variables in the pricing model. |
2.Institutions shall calculate the delta credit spread risk sensitivities for all securitisation and non-securitisation positions as follows:
S_{\mathrm{CS}_{kt}} = \frac{\mathrm{V}_{i} \left(\mathrm{CS}_{kt} + 0.0001, x, y \dots \right) - \mathrm{V}_{i} \left(\mathrm{CS}_{kt}, x, y \dots \right)}{0.0001}
where:
S_{\mathrm{CS}_{kt}} = the delta credit spread risk sensitivities for all securitisation and non-securitisation positions; |
cs_{kt} = the value of the credit spread rate of an issuer j at maturity t; |
V_{i} (.) = the pricing function of instrument i; and |
x,y = risk factors other than cs_{kt} in the pricing function Vi. |
3.Institutions shall calculate delta equity risk sensitivities as follows:
S_k = \frac{V_i(1.01 \mathrm{EQ}_k, x, y, \dots) - V_i(\mathrm{EQ}_k, x, y, \dots)}{0.01}
the sensitivities to risk factors consisting of equity spot prices shall be calculated as follows:
where:
s_{k} | = | the sensitivities to risk factors consisting of equity spot prices; |
k | = | a specific equity security; |
EQk | = | the value of the spot price of that equity security; |
V_{i} (.) | = | the pricing function of instrument i; and |
x,y | = | risk factors other than EQk in the pricing function Vi; |
S_{x_k} = \frac{V_i(\bar{x}_{ki} + 0.0001\bar{I}_m, y, z \dots) - V_i(\bar{x}_{ji}, y, z \dots)}{0.0001}
the sensitivities to risk factors consisting of equity repo rates shall be calculated as follows:
where:
S_{\mathrm{x}_{k}} | = | the sensitivities to risk factors consisting of equity repo rates; |
k | = | the index that denotes the equity; |
\bar{x}_{ki} | = | a vector of m components representing the repo term structure for a specific equity k with m being equal to the number of repo rates corresponding to different maturities used in the pricing model of instrument i; |
\overline{\mathrm{I}}_m | = | the unity matrix of dimension (1 · m); |
V_{i} (.) | = | the pricing function of the instrument i; and |
y,z | = | risk factors other than \bar{x}_{ki} in the pricing function Vi. |
4.Institutions shall calculate the delta commodity risk sensitivities to each risk factor k as follows:
S_k = \frac{V_i (1.01 \mathrm{CTY}_k, \gamma, z\dots) - V_i (\mathrm{CTY}_k, \gamma, z\dots)}{0.01}
where:
s_{k} = the delta commodity risk sensitivities; |
k = a given commodity risk factor; |
CTY_{k} = the value of risk factor k; |
V_{i} (.) = the pricing function of instrument i; and |
y, z = risk factors other than CTY_{k} in the pricing model of instrument i. |
5.Institutions shall calculate the delta foreign exchange risk sensitivities to each foreign exchange risk factor k as follows:
S_{k} = \frac{\mathrm{V}_{i}(1.01 \mathrm{FX}_{k}, y, z \dots) - \mathrm{V}_{i}(\mathrm{FX}_{k}, y, z \dots)}{0.01}
where:
s_{k} = the delta foreign exchange risk sensitivities; |
k = a given foreign exchange risk factor; |
FX_{k} = the value of the risk factor; |
V_{i} (.) = the pricing function of instrument i; and |
y, z = risk factors other than FX_{k} in the pricing model of instrument i. |