N.Y. Comp. Codes R. & Regs. tit. 11 § 44.10

Current through Register Vol. 46, No. 45, November 2, 2024

Section 44.10 - Examples

This section contains examples of the application of market-value adjustment formulae that meet the requirements of this regulation.

MARKET VALUE ADJUSTMENT EXAMPLES

Variables

x^A_t = Actual Accumulation Amount at time t derived from contribution made at time x

W_t = Withdrawal Charge Factor at time t

CSB_t = Cash Surrender Benefit at time t

(a)Single premium contracts.

(1) Internal index.

Example 1:

Five-year guaranteed interest rate contract.

Assume a contract issued three years ago with a five-year guaranteed interest rate of 12%. Currently, two-year single premium contracts are issued with a two-year guaranteed interest rate of 10%.

The current cash surrender benefit is determined to be:

(i) CSB₃ = (1 W₃) 0^A3 x ^1.122/_1.102

Alternatively:

(ii) CSB₃ = (1 W ₃)(0^A3)[1 (.10 .12) x 2]

Example 2:

Five-year guaranteed interest rate contract with cap.

Assume a contract issued three years ago with a guaranteed interest rate of 12% in years 1-5, and a minimum interest guarantee of 5% in years 6-10. There is a 5% cap on market value adjustments. Currently, two-year guaranteed interest rates of 8% are being offered on similar contracts.

The current cash surrender benefit is determined to be:

CSB₃ = (1 W₃)0^A3 x ^1.122/_1.082 cap of 5%

= (1 W₃) 0^A3 * 1.05

(2) External index.

Example 3:

Five-year guaranteed interest rate contract.

Assume a contract issued two-years ago with a five-year guaranteed interest rate of 9%. At issue, the yield to maturity on five-year Treasury bills was 10%. Currently, three -year Treasury bills are yielding 12% to maturity.

The current cash surrender benefit is determined to be:

(i) CSB₂ = (1 W₂)0^A2 x ^{1.10 3}/_1.123

Alternatively:

(ii) CSB₂ = (1 W ₂)(0^A2)[1 (.12 .10) * 3]

(b) Flexible premium contracts.

(1) Internal index.

Example 4:

Five-year flexible premium guaranteed interest rate contract.

Assume a contract issued three years ago, and the guaranteed interest rates to maturity (five years from issue) associated with deposits made during the first three contract years are as follows:

Time of deposit	Guaranteed interest rate to maturity
0	10%
1	9%
2	9%

Currently, two-year flexible premium contracts are issued with a guaranteed interest rate to maturity of 81/2% on first-year deposits.

The current cash surrender benefit is determined to be:

(i) CSB₃ = (1 W₃)(0^A3 x^1.102/_1.0852 + 1^A3 x ^1.092/_1.0852 + 2^A3 x ^1.092)/_1.0852

Alternatively:

(ii) Let i_avg = ^{0A3 * .10 + 1A3 * .09 + 2A3 * .09}/_{0A3 +1A3 + 2A3}

Then:

CSB₃ = [(1 W ₃) x ((0^A3 + 1^A3 + 2^A3) x (1 + i_avg)²)]/(1.085)²

Example 5:

Five-year flexible premium, flexible maturity guaranteed interest rate contract.

Assume a contract issued three years ago, and the guaranteed interest rates to maturity (five years from deposit) associated with deposits made during the first three contract years are as follows:

Time of deposit	Guaranteed interest rate to maturity
0	10%
1	10%
2	11%

Currently, the following guaranteed interest rates are offered on deposits to new issues of similar contracts:

Years to maturity	Guaranteed interest rate to maturity
2	8%
3	9%
4	10%

The current cash surrender benefit is determined to be:

(i) CSB₃ = (1 W₃)(0^A3 x^1.102/_1.082 + 1^A3 x ^1.103/_1.093 + 2^A3 x ^1.114)/_1.104

(ii) CSB₃ = (1 W ₃)[(0^A3)[1 (.08 .10) * 2]

+ (1^A3)[1 (.09 .10) x 3]

+ (2^A3)[1 (.10 .11) x 4]]

Alternatively:

Let n_avg = ^{(0A3 x 2) + (1A3 x 3) + (2A3 x 4)}/_{(0A3 + 1A3 + 2A3}

Assume n_avg = 3, Then:

(iii) CSB₃ = (1 W ₃)(0^A3 x 1.10³ + 1^A3 x 1.10 ³ + 2^A3 x 1.11³)/1.093

(2) External index.

Example 6:

Five-year flexible premium guaranteed interest rate contract.

Assume a contract issued three years ago with a five-year guaranteed interest rate of 9%. The yield to maturity on Treasury bills during this period was as follows:

Time	Years to maturity	T-bill yield to maturity
0	5	10%
1	4	9%
2	3	9%

Currently, two-year Treasury bills are yielding 81/2% to maturity.

The current cash surrender benefit is determined to be:

CSB₃ = (1 W₃)(0^A3x ^1.102/_1.0852+ 1^A3 x ^1.092/_1.0852+ 2^A3 x^1.092)/_{1.085 2}

Example 7:

Five-year flexible premium, flexible maturity guaranteed interest rate contract.

Assume the same facts as in example 6, and further assume that the following market values of $1,000, semiannual coupon Treasury bills are known:

Time	Years to maturity	Annual coupon rate	Market value
0	5	10%	$1,000
1	5	10%	$1,000
2	5	11%	$1,000
3	2	10%	$1,100
3	3	10%	$1,100
3	4	11%	$1,200

The current cash surrender benefit is determined to be:

CSB₃ = (1 W₃)(0^A3 x ¹¹⁰⁰/₁₀₀₀ + 1^A3 x¹¹⁰⁰/₁₀₀₀ + 2^A3 x ¹²⁰⁰⁾/₁₀₀₀

N.Y. Comp. Codes R. & Regs. Tit. 11 § 44.10