The Payment Model

The payment model gives the projected expected cashflows, allowing for decrements, in each remaining year of the term of the policy. From these, the policy liability of the portfolio can be calculated at discrete points in time. Assuming that premiums and expense (including commission) cashflows all occur at the beginning of the policy year, and that death, surrender and maturity benefit cashflows are all paid at the end of policy year, the following equations can be used to project these cashflows:

Beginning of Year t Cashflows

Premiums:

P remiums(t) =Px,t×Ex,t; (8.15)

where Px,t denotes the premium rate for lives agedx in year t. Premium rates are

156 Solvency Testing Methodology to those used in determining the policy liabilities) and the equation of value,

EPV (Premiums) = EPV (Benefits) + EPV (Expenses) + EPV (Profits). (8.16) Depending on the conditions of the policy, premiums may be constant for the entire term of the policy, or increase with age and/or due to inflation.

For Type 2 investment-linked policies, the premiums paid by the insurer are invested in a managed fund and returned to the policyholder, with interest, upon death or surrender. To cover their expenses and an allowance for profits, the insurer deducts fees from the accumulated premium amount at various points throughout the life of the policy (most commonly, on policy entry, on policy anniversaries, and at policy termination). The premium amount is generally determined by the policyholder, while the policy fees are determined based on the equation of value,

EPV (Fees) = EPV (Expenses) + EPV (Profits). (8.17)

Thus,

EPV (Premiums less Fees) + EPV (Fees)

= EPV (Benefits) + EPV (Expenses) + EPV (Profits). (8.18) Fees may be charged at the beginning of the year or at the end of the year, so may constitute beginning of year or end of year cashflows. For fees charged at the beginning of the year:

F eesboy(t) =Fboy(t)×Ex,t; (8.19)

and for fees charged at the end of the year:

F eeseoy(t) =Feoy(t)×Ex,t+1; (8.20) where Fboy(t) and Feoy(t) denote the fees charged per policy at the beginning and

end of yeart respectively, which may be expressed as a dollar amount per policy or as a percentage of the accumulated premiums received to date.

Expenses (including commission):

Expenses(t) =Expt×Ex,t; (8.21)

where Expt denotes the expenses, including commission, in yeart. Policy expenses

usually comprise a “dollars per policy” component, which is the same for all poli- cies of the same type, regardless of the size of the policy or characteristics of the policyholder, and a “percentage of premiums” component. The “dollars per policy”

Solvency Testing Methodology 157 expenses are usually assumed to increase with inflation.

Net Cashflows:

CFboy(t−1, t) =P remiums(t)−Expenses(t). (8.22)

End of Year t Cashflows

Death Benefits:

DB(t) = (SIt+Bonust)×Dx,t; (8.23)

whereSIt denotes the policy sum insured in yeartand Bonustdenotes the amount

of bonuses declared up to the end of year t. Depending on the policy conditions, the sum insured may be constant for the entire duration of the policy or increase in line with inflation, or investment earnings, in the case of investment-linked policies (other possibilities also exist, but are not considered in this thesis).

The declared bonuses component of the death benefits is only relevant in the case of participating or “with profits” policies (for non-participating policies,Bonust = 0,

for all t), and only traditional (Type 1) policies have ever been sold (in Australia) on a “with profits” basis. Bonus distribution rates are determined at the discre- tion of the insurer, based on a number of factors, including equity between different cohorts of policyholders, the reasonable expectations of policyholders and admin- istrative simplicity. As a result, it is very difficult to model a “typical” insurer’s bonus distribution policy, and consequently, all policies considered in this thesis are assumed to be non-participating.

Surrender Benefits:

SB(t) =SVt×Wx,t; (8.24)

whereSVt denotes the policy surrender value at timet. Surrender values are deter-

mined at the discretion of the insurer, subject to the minimum surrender amounts prescribed in LPS4.02, the Minimum Surrender Values and Paid-Up Values Stan- dard.

Maturity Benefits:

Maturity benefits are only paid if the policyholder survives to the end of the policy term. Thus, they are only paid once during the term of an insurance contract, if at all. Assuming the insurance contract matures at the end of year n, then

MB(n) = (MSIn)×Ex,n+1; (8.25)

whereMSIn denotes the maturity sum insured. This may be different from the sum

158 Solvency Testing Methodology Net Cashflows:

CFeoy(t−1, t) =−(DB(t) +SB(t) +MB(t)). (8.26)

BEL at the End of Year t

Again, assuming that the policy term expires at the end of year n,

BEL(t) =₋

n−1

X

k=t

(PVt(CFboy(k, k+ 1)) + PVt(CFeoy(k, k+ 1))) ; (8.27)

where PVt denotes the present value at time t, and the discount rate used is the

after-tax expected future investment earnings rate for Type 2 policies (where tax is assumed to be calculated at the current Australian corporate tax rate of 30%) and a “risk free” discount rate for all other policy types, as prescribed by LPS1.045_. The determination of the expected future investment earnings rate is discussed in Section 8.4.4.

Policy Liability at the End of Year t

Under LPS1.04, the policy liability at the end of year t is equal to the best esti- mate liability at the end of year t plus the expected present value of future best estimate bonuses (for participating business), plus the expected present value of fu- ture shareholder profits. However, for solvency testing purposes, it is usual to make no allowance for future shareholder profits (as was done in LPS2.04 and LPS3.04). Thus, for non-participating business, we set the policy liability at the end of year

t equal to the best estimate liability at that time. Participating policies are not considered in this thesis.

Taxation is not allowed for in the policy liabilities, with the exception of tax on investment earnings for Type 2 policies, because if an insurer is making no profits, it cannot be paying tax on them. For Type 2 policies, tax on investment earnings is allowed for by using an after-tax investment earnings rate throughout. That is, if

ig is the before-tax investment earnings rate, then the after-tax investment earnings

rate, in is determined by:

in =ig(1−tax rate). (8.28)

A tax rate of 30% is assumed throughout this thesis.

5

Under LPS1.04, “the gross rate used to discount expected future cashflows must, to the ex- tent the benefits under the policy are contractually linked to the performance of the assets held, reflect the expected investment earnings applicable to the assets backing the benefit being valued. Otherwise a risk free discount rate is to be used”.

Solvency Testing Methodology 159