ASC475/SAK/DEC2013

CHAPTER 5 : NON-FORFEITURE OPTIONSReference : Chapter 16 “ Actuarial Mathematics” , Bowers, Gerber, Hickman, SOA.

NONFORFEITURE CLAUSE

It allows the insured to stop making premium payments without forfeiting the policy benefits. The insured may receive a portion of the benefits or the full benefit or a partial refund of the premiums upon exercising the option provided by the clause. Various non-forfeiture options are available, the most common being:

1. Cash Surrender Value Option.2. Reduced Paid-Up Option.3. Extended Term Insurance Option.

Without exercising the clause, an insured who misses premium payments would forfeit the benefits of the policy after exceeding the grace period to settle the outstanding premiums. The policy would lapse.

5.1. CASH SURRENDER VALUE OPTION

The policy is surrendered to the insurance company in return for a cash surrender value(CSV) at the time ofsurrender. Upon surrender, the policy is cancelled.

In the USA, the CSV is based on the adjusted net level premium reserve where the CSV at time k=1,2,3,... is given by

kCV= A(k) – Pa ӓ(k)

where A(k) is the APV at time k of future benefits,

Pa ӓ(k) is the APV at time k of premiums of amount Pa payable annually in advance, Pa is the adjusted premium under USA 1980 Std Law.

Pa = [ A(0) +E1 ]/ ӓ(0)

= P + E1/ ӓ(0).

E1 = 1.25 x Min[P,0.04] +0.01.

Thus for :

A whole life policy issued to (x): kCVx = Ax+k - Pa ӓx+k ,

where Pa = Px + E1/ ӓx

An endowment policy issued to (x) : kCVx:n = Ax+k:n-k - Pa ӓx+k:n-k ,

where Pa = Px:n + E1/ ӓx:n

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ASC475/SAK/JUN2013

Example 1:

A $1000 25-yr endowment policy to (40) with benefit payable at the end of the year of death is paid by annual premium at the beginning of each policy year.Assuming DM’s Law with ω = 80 and i = 0.05. Find i) the 10th (terminal) reserve and ii) the 10th cash surrender value.

5.2. PAID-UP INSURANCE OPTION

The cash value at the time of exercising the option is used to pay as a single premium for a reduced amount of insurance. There are no more future premiums. The contract type and period of coverage remains the same.The amount of benefit is reduced.

5.2.1 CV based on the net level premium reserve

The reserve at time k, kV = bk A(k), where bk is the reduced sum assured.

Thus, bk = kV/A(k).

i) For $1, WL to (x), bk = kVx / Ax+k = kWx

Standard actuarial notation for bk based on $1 original SA and net level premium reserve = kW.

ii) For $1, n-yr Endowment to (x), bk = kVx:n / Ax+k:n-k = kWx:n

5.2.2 CV based on the CSV using the USA 1980 Std Law

The cash surrender value at time k, kCV = bk A(k).

Thus, bk= kCV/ A(k).

5.2.3 Treatment of outstanding loan on the policy

If there is an outstanding loan of amount L, the CV is reduced by the amount L.

i) CV is based on the net level premium reserve: kV – L = bk A(k)

ii) CV is based on the 1980 Std Law on Cash Surrender Value: kCV – L = bk A(k)

Example 2:

A $50,000, 20-yr endowment insurance is issued to (40). After 10 years, the policy has an outstanding loan of $5000 ( due to unpaid premiums before the expiry of the grace period). Assume DM’s Law with ω = 100 and δ = 0.05. Calculate the reduced benefit amount if the insured wishes to exercise the paid-up insurance option based on i) the net level premium reserve as the single premium, ii) the cash surrender value as the single premium.

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3. Extended Term Insurance Option

The cash value (less any outstandung loan) is used to pay for a term insurance policy equal to the face amount of the policy. The coverage continues for as long as the available cash value can buy.

Thus, under this option,

The policy is converted to term insurance, for a term of coverage determined by the available cash value, The sum assured remains the same as the original policy.

If the insured wishes to exercise this option at time k, then

S. kCV = S. Ax 1

+ k : h , where S is the original sum assured and h is the period of coverage on the term policy. Solve for h.

If there is an outstanding loan(o/s) of amount L, then the equation becomes:

S. kCV - L = (S – L). Ax 1+ k : h

3.1 In the case where the original policy is an n-yr endowment insurance, h may exceed the original coverage term, ie h > n-k

The cash value buys term insurance up to maturity (h=n-k) and a pure endowment (PE) payable upon survival at time n. The amount of PE is the difference between the cash value at time k and the APV of term benefits for the duration n-k.

i) S. kCV = S. Ax 1+ k : n-k + (PE) Ax + k : n

1-k

PE = [ S. kCV - S. Ax 1+ k : n-k ] / Ax + k : n

1-k with no o/s loan.

ii) S. kCV - L = (S – L). Ax 1+ k : n-k + (PE) Ax + k : n

1-k

PE = [S. kCV - L - (S – L). Ax 1+ k : n-k ] / Ax + k : n

1-k with o/s loan L.

Example 3: A $50,000 20-year endowment policy is issued to (40). After 10 years, there is an outstanding loan of $5,000. Use ILT@6% interest. The insured wishes to exercise the extended term option. Determine the term of coverage and, if there is any pure endowment benefit available at the end of the term.

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