Article 325r - Delta risk sensitivities

1.Institutions shall calculate delta general interest rate risk (GIRR) sensitivities as follows:

(a)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 V_i;

(b)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 V_i.

3.Institutions shall calculate delta equity risk sensitivities as follows:

(a)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;

EQ_k | = | 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 EQ_k in the pricing function V_i;

(b)S_{\mathrm{x}_{\mathrm{k}}} = \frac{\mathrm{V}_{\mathrm{i}}(\overline{\mathrm{x}}_{\mathrm{ki}} + 0.0001 \overline{\mathrm{I}}_{\mathrm{m}}, \mathrm{y}, \mathrm{z} \dots) - \mathrm{V}_{\mathrm{i}}(\overline{\mathrm{x}}_{\mathrm{ji}}, \mathrm{y}, \mathrm{z} \dots)}{0.0001}

the sensitivities to risk factors consisting of equity repo rates shall be calculated as follows:

where:

S_{\mathbf{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 V_i.

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 marketpricing valuefunction of instrument i as a function of risk factor k;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 marketpricing valuefunction of instrument i as a function of the risk factor k;i; and

y, z = risk factors other than FX_k in the pricing model of instrument i.