A Comparison of the Vasicek and Cox, Ingersoll, and Ross Interest Rate Models in Valuation of Insurance Assets, Liabilities and Surplus

Insurance Company’s cash flows are subjected to the risk of interest rate (C-3 risk). To curb the effect of this risk, Insurance companies normally adopts an interest period model that predicts the movement of the rates of interest. The most common models adopted by the Insurance Companies are the vasicek (1977) model and The Cox, Ingersoll and Ross (1985) Model. These two models are stochastic single period short-rate models; however, they exhibit different assumptions and because of this, the future values of insurance Assets and liabilities are likely to differ when these models are applied to estimate their values. Valuing of Insurance Assets and liabilities, especially in the Kenyan market is very challenging because of the tremendous fluctuations of interest rates as a result of gradual increments of the rate of inflation. In order for insurance companies to correctly value their insurance policies, they need to have a substantive Knowledge of their cash flows. The current valuation methods of insurance assets, liabilities and Surplus based on a stochastic interest rate models do not consider the possibility of occurrence of model risk, and therefore there is a possibility of either under estimating the future values of insurance assets and liabilities or over estimating. In this research paper, Geometric simulation was used to explore the effect of model risk By creating a comparison between The vacisek and the Cox, Ingersoll and Ross interest rate model. First, we evaluated the value of an insurance company’s assets and liabilities by assuming that the interest rate process is followed by the Cox, Ingersoll and Ross model and The vasicek (1977). Model risk arose by the different Values obtained for both the vacisek and the Cox, Ingersoll and Ross model. The results of the simulation showed that the cox, Ingersoll and Ross interest rate model provided a better fit of interest as compared to The Vasicek model.