Sec. 43.9. Examples

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

MARKET VALUE ADJUSTMENT EXAMPLES

Variables

_xPV _t = Unborrowed portion of the policy value at time t derived from contribution made at time ×

_xSC _t = Surrender Charge applicable at time t derived from contribution made at time ×

CSB_t = Cash Surrender Benefit at time t

LA_t = Value of Loan Account at time t

I_t = Amount of Indebtedness at time t

L_t = Loan requested at time t

(a) Single premium policies.

(1) Internal index.

Example 1:

Five-year guaranteed interest rate policy.

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

The current cash surrender benefit is determined to be:

(i) CSB₃ = ₀PV₃ × ^1.122/_1.102 + LA₃ − I₃ − ₀SC₃

Alternatively:

(ii) CSB₃ = ₀PV ₃[1 − (.10 − .12) × 2] + LA₃ − I₃ − ₀SC₃

Example 2:

Five-year guaranteed interest rate policy with cap.

Assume this policy was 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 policies.

The current cash surrender benefit is determined to be:

CSB₃ = ₀PV₃ ×^{1.12 2}/_1.082 cap of 5% + LA₃ − I₃ − ₀SC₃

= ₀PV₃ × 1.05 + LA ₃ − I₃ − ₀SC₃

(2) External index.

Example 3:

Five-year guaranteed interest rate policy.

Assume this policy was 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) CBS₂ = ₀PV₂ × ^1.103/_1.123 + LA₂ − I₂ − ₀SC₂

Alternatively:

(ii) CSB₂ = ₀PV ₂[1 − (.12 − .10) × 3] + LA ₂ − I₂ − ₀SC₂

(b) Flexible premium policies.

(1) Internal index.

Example 4:

Five-year flexible premium guaranteed interest rate policy.

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

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

Currently, two-year flexible premium policies are issued with a guaranteed interest rate to maturity of 8½% on first year deposits.

The current cash surrender benefit is determined to be:

(i) CSB₃ = ₀PV₃ × ^1.102/_1.0852 + ₁PV₃ × ^1.092/_1.0852

+ ₂PV₃×

^1.092/_1.0852 + LA₃ − I₃ − (₀SC₃ +₁SC₃ + ₂SC ₃)

Alternatively:

(ii) Let ⁱ_avg =₀PV ₃ × .10 + ₁PV₃ × .09 + ₂PV₃ × .09/₀PV₃ + ₁PV₃ + ₂PV₃

Then:

CSB₃ = [(₀PV₃ + ₁PV₃ + ₂PV₃) × (1 + ⁱ_avg))[/(1.085) + LA ₃= I₃ − (₀SC₃ + ₁SC₃ +₂SC₃)

Example 5:

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

Assume this policy was issued three years ago, and the guaranteed interest rates to maturity (five years from deposit) associated with deposits made during the first three policy 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 policies:

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 = ₀PV₃ × ^1.102/_1.082

+₁ PV₃ × ^1.103/_1.093

+ ₂PV₃ ×

^1.114/_1.104 + LA₃ − I₃ − (₀SC₃ +₁SC₃ + ₂SC ₃)

(ii) CSB₃ = ₀PV ₃[1 − (.08 − .10) × 2[ +

₁PV₃[1 − (.09 − .10) × 3[ + ₂PV ₃[1 − (.10 − .11) × 4[

+ LA₃ − I₃ − (₀SC ₃+₁SC₃ + ₂SC₃)

Alternatively:

Letⁿ_avg = ₀PV ₃ × 2 +₁PV₃ × 3 + ₂PV₃ × 4/( ₀PV₃ +₁PV₃ + ₂PV ₃)

Assume ⁿ_avg= 3

Then:

(iii) CSB₃ = ₀PV ₃ × 1.10 +₁PV₂ × 1.10 + ₂PV₃ × 1.11/_1.093

+ LA₃ − I₃ − (₀SC₃ +₁SC₃ + ₂SC ₃)

(2) External index.

Example 6:

Five-year flexible premium guaranteed interest rate policy.

Assume this policy was 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 8 ½% to maturity.

The current cash surrender benefit is determined to be:

CSB₃ = ₀PV₃ × ^{1.10 2}/_1.0852 +₁PV₃ ×

^1.092/_1.0852

+ ₂PV₃ × ^1.092/_1.0852

+ LA₃ − I₃(₀SC₃+₁SC₃ + ₂SC₃)

Example 7:

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

Assume the same facts as in example 6, and 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 = ₀PV₃ × /₁₀₀₀ +₁PV₃× /₁₀₀₀

+ ₂PV₃ ×

/₁₀₀₀ + LA₃− I₃ − (₀SC₃ +₁SC ₃ + ₂SC₃)

(c) Loan activity.

A prime (′) indicates a value immediately prior to loan activity.

(1) Internal index.

Example 8:

Five-year guaranteed interest rate contract.

Assume a policy issued three years ago with a five-year guaranteed interest rate of 10%. Currently, two-year single premium policies are issued with a two-year guaranteed interest rate of 8%. Loan is made at the end of the third year.

₀PV₃ = ₀PV′₃ − L ₃ ×^(1.08)2/_(1.10)2

LA₃ = LA′₃ + L₃

I₃ = I′₃ + L₃

CSB₃ = ₀PV₃ × ^(1.10)2/_(1.08)2 + LA₃ − I₃ − ₀SC₃

(2) External index.

Example 9::

Five-year guaranteed interest rate contract.

Assume a policy 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 13% to maturity. Loan is made at the end of the second year.

₀PV₂ = ₀PV′₂ − L ₂ ×^(1.13)3/_(1.10)3

LA₂ = LA′₂ + L₂

I₂ = I′₂ + L₂

CSB₂ = ₀PV₂ × ^(1.10)3/_(1.13)3 + LA₂ − I₂ − ₀SC₂