Benefit Payments

Benefit Payments represents the contractual obligation that the insurers needed to pay to policyholders upon some predefined events.

For example, if the policyholder died, they will receive the death benefit (DB); when they lapsed, they will receive guarantee cash value (GCV) / surrender benefit; when the policy matured, they will receive maturity benefit (MB).

To summarize, guarantee insurance benefits can be summarized in the following matrix:

Here is the introduction for each of the benefit:

Coupon Benefit: This is an annuity like, guarantee cash benefit paid to the policyholder. For some company, this benefit will combine with maturity benefit and called "Survival Benefit".

Death Benefit: This is the death benefit paid to the policyholder upon death.

Surrender Benefit / Guarantee Cash Value: This is the amount to be paid to the policyholder when he / she lapsed. It is also called "Guarantee Cash Value" because it represents the minimum value of the contract the policyholder can get, regardless of insured events.

Maturity Benefit: This is the maturity benefit paid to the policyholder when the contract mature.

Critical Illness Benefit: This is the CI benefit paid to the policyholder upon diagnosed diseases.

The calculation for benefit is defined by:

\begin{equation}
\begin{split}
Benefit\_Outgo _t & = Benefit\_PP _t × NO\_STATES _t
\end{split}
\end{equation}

While the equation is simple, devil is in the detail. The hardest part of the calculation is on the "Benefit Per Policy (Benefit_PP)" calculation. We will introduce the PP calculation for some benefit in later chapters.

A simpler example using death benefit shows how the above formula should be applied. Assume a insurance contract pays the Face Amount (FA) upon the death of the policyholder. Then the death outgo is calculated by:

\begin{equation}
\begin{split}
DTH\_OUTGO _t & = DB\_PP _t × NO\_DEATHS _t \\
& = FA × NO\_DEATHS _t
\end{split}
\end{equation}

Let's go through a practical example below:

We shall use the same double decrement model we have introduced in previous chapters. Assume the Face Amount (FA) is 500. The number of policies as well as benefit per policy amount is given in the following table:

Assume coupon benefit is a BOP cashflow and maturity benefit is a EOP cashflow.

Year 1

DTH_OUTGO = DB_PP * NO_DEATHS = 500 * 0.000174 = 0.09

SURR_OUTGO = GCV_PP * NO_SURRS = 50 * 0.099991 = 5.00

COU_OUTGO = CB_PP * NOP_IFSM = 0 * 1 = 0

MAT_OUTGO = MB_PP * NOP_IF = 0 * 0.899835 = 0

Year 2

DTH_OUTGO = DB_PP * NO_DEATHS = 500 * 0.000312 = 0.16

SURR_OUTGO = GCV_PP * NO_SURRS = 100 * 0.044984 = 4.50

COU_OUTGO = CB_PP * NOP_IFSM = 0 * 0.899835 = 0

MAT_OUTGO = MB_PP * NOP_IF = 0 * 0.854540 = 0

...

Year 10

DTH_OUTGO = DB_PP * NO_DEATHS = 500 * 0.000492 = 0.25

SURR_OUTGO = GCV_PP * NO_SURRS = 500 * 0.007850 = 3.92

COU_OUTGO = CB_PP * NOP_IFSM = 25 * 0.785212 = 19.63

MAT_OUTGO = MB_PP * NOP_IF = 500 * 0.776870 = 388.43

A demonstration spreadsheet showing the calculation above can be downloaded here:

https://drive.google.com/file/d/0B4OirwHLcmE1Ti1zVDJPYjRhUm8/view?usp=sharing