Technical Standards for the Determination of Necessary Technical Capital and Generation of Mortality Tables

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

THE COMMITTEE OF STANDARDS OF THE CENTRAL RESERVE BANK OF EL SALVADOR, CONSIDERING:
I. That by Legislative Decree No. 787, dated September 28, 2017, published in the Official Gazette No. 180, Volume No. 416 of the same date, the Reform to the Law of the Pension Savings System was approved.
II. That Article 87 of the Reform to the Law of the Pension Savings System cited in the previous consideration establishes that the Central Reserve Bank of El Salvador must prepare or update the relevant Technical Standards for the application of what is provided in the aforementioned Legislative Decree, no later than one hundred and eighty days counted from its validity.
III. That Article 119 of the Law of the Pension Savings System establishes that the necessary technical capital will be determined with the expected present value of the reference pensions of the deceased and their beneficiaries from the date the second ruling of invalidity is executed or the death occurs, and until the extinction of the right to pension of each of the accredited beneficiaries.

THEREFORE, by virtue of the regulatory powers conferred by Article 99 of the Law of Supervision and Regulation of the Financial System, AGREES to issue the following:

CHAPTER I
OBJECT, SUBJECTS AND TERMS

Object
Art. 1.- These Standards aim to establish the technical specifications, including variables, formulas, and tables to be used for the calculation of the necessary technical capital for the affiliate and their group of beneficiaries.

Subjects
Art. 2.- The subjects obliged to comply with these Standards are the Pension Fund Administrators (AFP).

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

Terms
Art. 3.- For the purposes of these Technical Standards, the terms indicated below have the following meaning:
a) AFP: Pension Fund Administrators; b) Central Bank: Central Reserve Bank of El Salvador; c) CIAP: Individual Savings Account for Pensions; d) CTN: Necessary Technical Capital, which is the expected present value of the reference pensions of the deceased and their beneficiaries from the date the second ruling of invalidity is executed or the death occurs, and until the extinction of the right to pension of the affiliate and each of the accredited beneficiaries; e) ctn: Necessary technical capital to finance one unit of pension; f) Affiliate's reference pension: That determined as a percentage of the Regulator Basic Salary applicable for any time of service the affiliate may have rendered; g) Beneficiaries' reference pension: That obtained by multiplying the reference pension of the deceased by the percentage corresponding to each beneficiary; h) Regulator Basic Salary: The monthly average of the Contribution Base Income calculated in accordance with the Law of the Pension Savings System; i) SAP Law: Law of the Pension Savings System; and j) Superintendence: Superintendence of the Financial System.

CHAPTER II
CALCULATION OF NECESSARY TECHNICAL CAPITAL

Designations
Art. 4.- The AFPs, for the purposes of calculating CTN and ctn, will use the following designations:
x : Age of the pension originator; y : Age of the spouse, partner, father, or mother of the originator; z : Maximum age limit for normal children with right to pension, i.e., 24 years; h : Age of the child; hm : Age of the youngest child; hi : Age of the invalid child; Dx : Represents the present value of one monetary unit for each of the ages of the originator; Nx : Represents the total present value of one monetary unit for all Dx; Dxy : Represents the present value of one monetary unit for each of the ages of the originator given the probability that the respective beneficiary lives; in the case of beneficiaries, they are represented by the subscripts y, z, hm, hi; Nxy : Represents the total present value of one monetary unit for all Dxy; CTN : Necessary Technical Capital; ctn : Necessary technical capital to finance one unit of pension;

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

v_x : Update factor; i : Annual interest rate, used to establish commuted values in tables; SBR : Regulator Basic Salary; and l_x, l_y : Number of living persons at a given age.

Equalities
Art. 5.- The AFPs, for the purposes of calculating CTN and ctn, will use the following equalities:
Dx = v_x^x . l_x [1]
N_x = Σ Dx [2]
Dxy = v_x^x . l_x . l_y [3]
N_xy = Σ Dxy [4] v_x = 1 / (1 + i) [5]

Determination of Necessary Technical Capital per unit of pension Art. 6.- The AFPs, for the determination of the ctn formulas, will use actuarial theory through the development of actuarial functions and commuted values, which allow, from the mortality table and an interest rate, to determine the present value of future benefits in a rapid and effective manner.

Art. 7.- The AFPs must establish the ctn factor according to the characteristics of the pension originator according to the different calculation formulas described below:

1. Pension originator due to permanent disability.
   ctn = (N_x - N_24) / (D_x - D_11) [6]

2. The spouse, partner, when there are no non-invalid children with right to pension or there is one or more invalid children, or father and mother of a pensioner due to permanent disability.
   ctn = (N_y - N_24) / (D_y - D_11) - (N_xy - N_24) / (D_xy - D_11) [7]

3. The spouse, partner, with children with right to pension, when it concerns pensions due to disability. Provided that there are no invalid children within the group of beneficiaries.

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

4. Non-invalid child of the originator, with right to pension (if and only if: z – h > 0), when it concerns pensions due to disability.
   ctn = [ (N_xh - N_x(z-h)) / (D_xh - D_11) ] - [ (N_x(z-h) - N_x(z-h-z+h)) / (D_x(z-h) - D_11) ] [9]

5. Invalid child of the originator, with right to pension, when it concerns pensions due to disability.
   ctn = (N_hi - N_24) / (D_hi - D_11) - (N_xhi - N_24) / (D_xhi - D_11) [10]

6. Spouse or partner of a deceased affiliate, when there are no children with right to pension, or the children are invalid, or for the father and mother of a deceased affiliate.
   ctn = (N_y - N_24) / (D_y - D_11) [11]

7. Spouse or partner of a deceased affiliate, when there are no invalid children and there are children with right to pension.
   ctn = [ (N_y - N_24) / (D_y - D_11) ] + 0.20 [ (N_yz-hm - N_yz-hm) / (D_yz-hm - D_11) ] [12]

8. Non-invalid children of a deceased affiliate.
   ctn = (N_y - N_z-h) / (D_y - D_11) [13]

9. Invalid children, invalid father or mother of a deceased affiliate.
   ctn = [ (N_xy - N_24) / (D_xy - D_11) ] + 0.20 [ (N_yz-hm - N_yz-hm) / (D_yz-hm - D_11) ] + [ (N_xz-hm - N_xz-hm) / (D_xz-hm - D_11) ] + [ (N_yz-hm - N_yz-hm) / (D_yz-hm - D_11) ] + [ (N_xz-hm - N_xz-hm) / (D_xz-hm - D_11) ] [8]

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

ctn = (N_hi - N_24) / (D_hi - D_11) [14]

When calculating the ctns, it must be done with eight digits of approximation.

Determination of Necessary Technical Capital
Art. 8.- The AFPs, to determine the CTN required to finance a pension, will apply the following formula:
a) If the reference pension is greater than or equal to the current minimum pension:
CTN = ctn x 12.5 x reference pension [15] (2) b) If the reference pension is less than the current minimum pension:
CTN = ctn x 12.5 x current minimum pension [15 A] (3)

To determine the total CTN, it is necessary to sum the CTN of the affiliate and that of each of their beneficiaries.
When it comes to survivorship pensions, the total CTN will be the sum of the CTN of each of the beneficiaries.

Reference Pensions
Art. 9.- For the calculation of the CTN, the reference pension of the originator for the payment of disability pensions, as well as the reference pensions of the beneficiaries of survivorship pensions, will be determined in accordance with what is established in Articles 120 and 121 of the SAP Law.

For the calculation of the reference pensions of the affiliate or originator, the provisions relative to the final clause of Article 120 of the SAP Law must be applied, which establishes that when the resulting calculation of the reference pensions is lower than the value of the current minimum pensions for disability or survivorship, these must be adjusted to said minimum amounts. (2)

CHAPTER III
GENERATION OF MORTALITY TABLES AND APPLICABLE INTEREST RATE

Generation of mortality tables
Art. 10.- The formulas to determine the ctns have been expressed in terms of commuted functions, being necessary the use of analytical functions that allow generating the mortality tables. These analytical functions are presented as a function of qx which corresponds to the probability that a person of age x dies within a year, that is:
q_x = l_{x+1} / l_x => q_x = d_x / l_x [16]

The mathematical function used for the generation of qx values in mortality tables is expressed as follows:
q_x = 1 - s * g^{(c-1)^x} [17]

For all tables when the age is 110 years, qx will be equal to 1.

Annex No. 1 of these Standards contains the parameters necessary for the generation of the mortality tables.

Applicable Interest Rate
Art. 11.- The applicable interest rate that will be used for the generation of the mortality tables will be 4%, tables corresponding to Annex No. 2 of these Standards.

This rate will be reviewed with a periodicity of every three (3) years by the Committee of Standards of the Central Bank, in accordance with the average profitability of the Pension Funds.

CHAPTER IV
OTHER PROVISIONS AND VALIDITY

Sanctions
Art. 12.- Non-compliance with the provisions contained in these Standards will be sanctioned in accordance with what is established in the Law of Supervision and Regulation of the Financial System.

Repeal
Art. 13.- These Standards repeal the SAP Instruction No. 29/98 for the “Determination of Necessary Technical Capital and Generation of Mortality Tables” approved by Resolution No. A-DO-AF-052/98 of June 10, 1998 and Resolution A-AF-DO-485/99 of November 4, 1999 which substituted the RVHES table annexed to SAP Instruction No. 29/98, both issued by the Superintendence of Pensions whose Organic Law was repealed by Legislative Decree number 592 which contains the Law of Supervision and Regulation of the Financial System, published in the Official Gazette number 23, Volume 390 of February 2, 2011.

Art. 14.- These Standards render ineffective from the entry into force of these the “Resolution on the establishment of the technical interest rate for the calculation of the necessary technical capital”

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

issued in resolution number 14, of the Directing Council Session of the Superintendence of the Financial System No.CD-54/2017, dated December 12, 2017.

Transitional for affiliates with requirements met to access old-age benefits prior to the validity of Legislative Decree No. 787 Art. 14-A.- For those affiliates who, upon the entry into force of Legislative Decree No. 787, that is, on October 6, 2017, had met the requirements to access an old-age pension and had not exercised their right and opt for their benefit calculations to be made with the methodology in force on the date of meeting the requirements according to what is established in the “Technical Standards for the Granting of Old-Age Benefits in the Pension Savings System” (NSP-06), for the purposes of establishing the amount of their pension, the ctn must be calculated in accordance with what is established in Annex No. 3 of these Standards. (1)

Unforeseen Matters
Art. 15.- The aspects not provided for in regulatory matters in these Standards will be resolved by the Central Bank through its Committee of Standards.

Validity
Art. 16.- These Standards will enter into force from February 9, 2018.

MODIFICATIONS:
(1) Modifications approved by the Committee of Standards of the Central Reserve Bank of El Salvador, in Session No. CN-02/2018, dated March 7, two thousand eighteen, with validity from March 9, two thousand eighteen. (2) Modifications approved by the Central Reserve Bank of El Salvador through its Committee of Standards, in Session No. CN-10/2018, dated October 19, two thousand eighteen, with validity from October 24, two thousand eighteen. (3) Modifications approved by the Central Reserve Bank of El Salvador through its Committee of Standards, in Session No. CN-15/2018, dated December 20, two thousand eighteen, with validity from December 21, two thousand eighteen.

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

Annex No. 1
PARAMETERS NECESSARY FOR THE GENERATION OF MORTALITY TABLES The parameters necessary for the generation of the mortality tables are the following:

1. The BH ES and BM ES tables of Annex No. 2, will be used for the calculation of the ctns corresponding to the beneficiaries of survivorship pensions.
   The parameters to be used are the following:
   i) BH ES (male beneficiaries)
   0 ≤ x < 70 70 ≤ x < 110 c = 1.08713806 c = 1.08974392 g = 0.99884852 g = 0.99912795 s = 0.99991596 s = 0.99680157

ii) BM ES (female beneficiaries)
0 ≤ x < 70 70 ≤ x < 110 c = 1.09616544 c = 1.10424985 g = 0.99966998 g = 0.99982389 s = 0.99988595 s = 0.99903395

2. The MI H ES and MI M ES tables of Annex No.2, will be used to calculate the ctns corresponding to invalid affiliates and invalid beneficiaries.
   The parameters to be used are the following:
   i) MI H ES (invalid males)
   0 ≤ x < 70 70 ≤ x < 110 c = 1.07498069 c = 1.08614559 g = 0.99715038 g = 0.99856960 s = 0.98532445 s = 0.99215459

ii) MI B ES (invalid females)
0 ≤ x < 70 70 ≤ x < 110

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

Annex No. 1
c = 1.08113936 c = 1.10096721 g = 0.99888793 g = 0.99968639 s = 0.99091746 s = 0.99680732

The mortality tables referred to in this section have been generated with the information provided for each of them.
Generally, for the creation of the tables, the following has been considered:

1. In all columns where multiplications are performed, the round formula has been used.
2. The values corresponding to qx have been approximated to 5 decimals.
3. The values corresponding to the update factor have been approximated to 8 decimals.
4. The rest of the columns have been rounded to zero decimals.

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

Annex No. 3
Determination of Necessary Technical Capital and Generation of Mortality Tables.
The AFPs will determine the Necessary Technical Capital in accordance with what is established in this Annex.

I) FORMULAS FOR THE CALCULATION OF ctn
The AFPs, for the determination of the ctn formulas, will use actuarial theory through the development of actuarial functions and commuted values, which allow, from the mortality table and an interest rate, to determine the present value of future benefits in a rapid and effective manner.

The applicable interest rate that will be used for the generation of the mortality tables will be six percent (6%), tables corresponding to this Annex.

The AFPs must establish the ctn factor according to the characteristics of the pension originator according to the different calculation formulas described below:

1. Pension originator due to old age.
   ctn = (N_x - N_24) / (D_x - D_11)

2. The spouse, partner, when there are no non-invalid children with right to pension or there is one or more invalid children, or father and mother of a pensioner due to old age.
   ctn = (N_y - N_24) / (D_y - D_11) - (N_xy - N_24) / (D_xy - D_11)

3. The spouse, partner, with children with right to pension, when it concerns pensions due to old age. Provided that there are no invalid children within the group of beneficiaries.
   ctn = [ (N_xy - N_24) / (D_xy - D_11) ] + 0.20 [ (N_yz-hm - N_yz-hm) / (D_yz-hm - D_11) ] + [ (N_xz-hm - N_xz-hm) / (D_xz-hm - D_11) ] + [ (N_yz-hm - N_yz-hm) / (D_yz-hm - D_11) ] + [ (N_xz-hm - N_xz-hm) / (D_xz-hm - D_11) ]

4. Non-invalid child of the originator, with right to pension (if and only if: z – h > 0), when it concerns pensions due to old age.

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

Annex No. 3
ctn = [ (N_xh - N_x(z-h)) / (D_xh - D_11) ] - [ (N_x(z-h) - N_x(z-h-z+h)) / (D_x(z-h) - D_11) ]

5. Invalid child of the originator, with right to pension, when it concerns pensions due to old age.
   ctn = (N_hi - N_24) / (D_hi - D_11) - (N_xhi - N_24) / (D_xhi - D_11)

6. Spouse or partner of a deceased affiliate, when there are no children with right to pension, or the children are invalid, or for the father and mother of a deceased affiliate.
   ctn = (N_y - N_24) / (D_y - D_11)

7. Spouse or partner of a deceased affiliate, when there are no invalid children and there are children with right to pension.
   ctn = [ (N_y - N_24) / (D_y - D_11) ] + 0.20 [ (N_yz-hm - N_yz-hm) / (D_yz-hm - D_11) ]

8. Non-invalid children of a deceased affiliate.
   ctn = (N_y - N_z-h) / (D_y - D_11)

9. Invalid children, invalid father or mother of a deceased affiliate.
   ctn = (N_hi - N_24) / (D_hi - D_11)

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

Annex No. 3
The number of decimals to be used for the calculation of the ctns is eight digits with normal approximation.

II) DETERMINATION OF CTN
In general terms, to determine the CTN required to finance a pension, the following formula will be applied:
CTN = ctn x 12.5 x reference pension. (2)

To determine the total CTN, it is necessary to sum the CTN of the affiliate and that of each of their beneficiaries.
When it comes to survivorship pensions, the total CTN will be the sum of the CTN of each of the beneficiaries.

III) GENERATION OF MORTALITY TABLES
The formulas to determine the ctns have been expressed in terms of commuted functions, being necessary the use of analytical functions that allow generating the mortality tables. These analytical functions are presented as a function of qx which corresponds to the probability that a person of age x dies within a year, that is:
q_x = l_{x+1} / l_x => q_x = d_x / l_x

The mathematical function used for the generation of qx values in mortality tables is expressed as follows:
q_x = 1 - s * g^{(c-1)^x}

For all tables when the age is 110 years, qx will be equal to 1.

Below are the parameters necessary for the generation of the mortality tables:

1. RV H ES and RV M ES tables, will be used for the calculation of the ctns corresponding to affiliates retiring due to old age.
   i) RV H ES (old age males)

NSP-05
Approval: 02/02/2018
Validity: 09/02/2018

Annex No. 3
0 ≤ x < 70 70 ≤ x < 110 c = 1.08958261 c = 1.09619240 g = 0.99927508 g = 0.99956741 s = 0.99973666 s = 0.99888792

ii) RV M ES (old age females)
0 ≤ x < 70 70 ≤ x < 110 c = 1.09843146 c = 1.11293478 g = 0.99978776 g = 0.99993164 s = 0.99983305 s = 0.99858218

2. The BH ES and BM ES tables, will be used for the calculation of the ctns corresponding to the beneficiaries of survivorship pensions.
   The parameters to be used are the following:
   i) BH ES (male beneficiaries)
   0 ≤ x < 70 70 ≤ x < 110 c = 1.08713806 c = 1.08974392 g = 0.99884852 g = 0.99912795 s = 0.99991596 s = 0.99680157

ii) BM ES (