Modern Premium and Reserve Calculation

KEY WORDS

Field of actuarial control Unbundled products Internal rate of return (IRR) Net present value Yearly renewable term insurance Profit test Level premium

In the previous chapter the traditional method of premium calculation was presented. It is characterised by the strict differentiation between net and gross premium, and by its dealing with the impact of relatively few factors. Nowadays modern methods of calculating premium are spreading, existing side by side with the traditional modes. The main feature of these methods is that through computer programme packages they can explicitly consider much more factors effecting the premium. Due o the nature of the subject they do not work with closed formulae, but with the method of trial and error: different assumptions are being varied until an ’’acceptable’’ and stable premium is calculated. In these models profit is the main outcome-variable, so the method itself is called profit test. In the followings, we introduce the main points of profit tests, and we show through a case study that using simple assumptions we can make such models for ourselves. 

1 THE PROFIT TEST

First profit testing programmes were made in actuarial consultative companies150 in order to check the calculations of clients, but it was soon realised that these are marketable products on their own. Profit testing programmes appeared at the time when unbundled products were spreading, which do not contain fixed elements (endowment, term fix, etc. – i.e. traditional life insurances as this book calls them), but they are constructed by visible elements (universal life, unit linked – modern life insurances as this book calls them). In these programmes all parts of the premium are visible and are handled like an account. (As we have seen, this is the combination of an account and a yearly renewable term = YRT insurance.) This development gave momentum to new pricing methods, because applying classical methods to these products is rather difficult (since classical methods of premium calculation were developed to ‘’suit’’ traditional products). The new methods made it necessary, while the development of the environment made it possible for new pricing methods to come into life. Main elements of the development of the environment are:

 1.  Opportunities provided by information technology.

 2. Given conditions (inflation, investment environment: shift from investment in bonds towards investments in shares). 

3. A state of competition in which insurance companies ’’found’’ themselves.

As we have already seen, the change of the environment in itself contributed to and reflected on the appearance of modern insurances. Modern principles used in the pricing process do not contradict the classic ones, but they are slightly rephrased. In case of modern techniques of premium calculation we do not talk about the principle of equivalence, but about the net present value of the premium being equal to zero, i.e. about the requirement of NPV(BP) =0.