|
Summary
Financial liberalization generally increases the volatility of the yields life insurance companies will earn on their assets under management. Such insurers must reduce this high volatility in an efficient manner. Corporate asset investment managers must therefore forecast the yield on an investment, its volatility, and the correlation between different asset investments. The inherent complexity of the financial market makes it extremely difficult to make such projections.
However, through the management of a life insurance company, we can understand how these three indicators are related to one another by using the OMNI model, which this paper is intended to delineate.
At the 26th ICA Convention in Birmingham, we gave the following presentation:
By way of example, suppose that a life insurance company now sells endowment insurance, endowment insurance with ten-fold-type term insurance, and term life insurance. The company's asset investment is expressed using interest rates based on open market rates and volatility. Suppose that there is a 0.5 coefficient of correlation between asset investments for endowment insurance and those for endowment insurance with ten-fold-type term insurance and term life insurance.
The open market rates follow the CIR model shown below.
The actuarial assumptions for guaranteed yields are as follows:
a) The assumed interest rate is 2.7 percent.
b) The assumed mortality rate is in accordance with the 16th population mortality table (qx+t; t=1～15).
c) The term of insurance is 15 years.
These basic assumptions are used to calculate the net premium. Premium tariff rates are determined by adding the assumed rate of expense to the net premium rate, but the actual expense may vary depending on the rate of inflation. The tariff premium is set at a level at which the probability of the asset share at maturity being below the amount to be accumulated stands at 10 percent. In other words, the tariff premium for each product is set at a level at which the probability of insolvency stands at 10 percent. By determining the optimum product share for each of these insurance products, the probability of insolvency can be reduced to four percent. This six-percentage-point decrease helps the insurance company to maintain a net-worth ratio of 0.4 percent and stabilize its management.
In addition, we explained the details of management stabilization and discussed other subjects. As part of the presentation, we illustrated that, in the case of endowment insurance, if the market structure follows the CIR (SR) model, dr=a(3,0%-r)dt+r0,5 dZ (where r is the interest rate and  is the standard deviation), there will be a low-risk, high-return situation. However, this kind of situation seldom occurs in the efficient financial market. We had one more problem as well: we calculated the optimum product share based on the assumption that assets will be separately managed for each insurance product, without clear demarcation between the asset and product portfolios.
The first problem was resolved at the Centenary Anniversary Convention of Japanese Actuaries, at which we evaluated an interest-rate structure equation by applying the OMNI model and demonstrated that, in the case of the CIR (SR) model, for example, 0.1 for a and 0.5 for , i.e., dr=0.1(3.0%-r)dt+r0.5 dZ, is appropriate. As regards the latter problem, in this paper we calculated, compared, and assessed the effectiveness of investment diversification for each of the asset and product portfolios. |
