Zillmerisation

Zillmerisation

Zillmerisation relates to the valuation of a Life insurer by an actuary.

When new business is written, the value of the company may reduce (when viewed on a regulatory basis) even if the business is likely to be profitable. This is known as New Business Strain. Zillmerisation is one method of adjusting a net premium valuation to ease this initial valuation strain.

History

This method was developed by August Zillmer in the late 1800s, and described in an 1863 paper entitled "Contributions to the Theory of Life Insurance Reserves".

Calculation

The process of 'Zillmerisation', or 'applying a Zillmer adjustment' involves increasing the amount of future net premiums allowed for in the valuation. The amount of the increase is notionally applied to recoup the initial acquisition and administrative costs. Over time, the Zillmer asset is amortised as the initial expenses are effectively recouped.

More specifically when doing a net premium valuation, for a policy taken at age x, t years into the policy:

reserve = S . A(x+t:n-t) - NP(x:n) a(x+t:n-t)

       = 0 at time t=0 (by definition of NP)

where S is the sum assured (face amount), A is an assurance function, NP is the net premium for that sum assured, a is an annuity function, E is the initial expenses (i.e. PV of future benefits less PV of future notional net premiums)

In applying a Zillmer adjsument, NP is increased by an amount E/a(x:n)

so that the reserve at time t=0 is -E

A variation on the Zillmer adjustment is the Sprague adjustment:

If we assume the first year of premium doesn't count (because it's being used up on those initial costs), we can change the reserve as follows:

reserve = A(x+t:n-t) - NP(x+1:n-1) a(x+t:n-t) (i.e. PV of future benefits less PV of different notional net prem)

Since the adjusted net premium is larger, you are in effect subtracting a larger amount, producing a smaller reserve - and thus reducing the new business strain.

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