Dwa sposoby modelowania stopy procentowej w ubezpieczeniach życiowych
Two ways of stochastic modelling of interest rate in life insurances

Summary/Abstract: In the traditional actuarial literature, to make it simple, it is assumed that the rate of interest is fixed and the same throughout the years. However, the interest rate that will apply in the future years is, of course, neither known nor constant. Therefore, the stochastic interest rate to the actuarial calculations is applied in the research. Two ways of stochastic modelling of interest rate: actuarial and financial are described in the article. The actuarial and financial ways of modelling of interest rate are distinguished according to applying the interest rate model. The actuarial calculations are presented in the case of the generalized life annuity payable m times a year at the end of each m-th of the year. In the actuarial way the expected value and the variance of the discount value of benefit payment are determined in a traditional way, and the technical stochastic interest rate models are applied to the calculations. In the financial way benefit payments are treated as a stochastic cumulative cash flow. The discount value of these cash flows is valuated under the assumption that arbitrage is not possible. To the actuarial calculations the models of short-term rate are applied. In the article four stochastic processes are used as interest rate models in life insurances. The analysis of the influence of stochastic interest rate on calculating net premiums, actuarial values of life annuities and net mathematical reserves is done. The results and conclusions are described in the last part of the article.

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