A comparison of Vasicek and Cox-Ingersol-Ross models in determination of reserves for a term assurance policy

Abstract

Interest rates influence the calculation of premiums, reserves and benefits in the long-term. Theoretically, calculation of such actuarial values is based on the assumption of constant interest rates although interest rates constantly move over time. To obtain a more realistic assessment in valuation, it is beneficial if stochastic interest rates are used. Accurate calculation of reserves ensures that the insurance company can pay claims. A Reserve is a sum of money held by a financial institution such as a life office or a pension fund to cover for the difference between present value of future liabilities including expenses and present value of future premiums. A term insurance contract is an insurance policy that pays the sum assured to the beneficiaries if the policyholder dies within the duration of the policy. The purpose of this study was to compare the reserves that would be needed for a term insurance policy using the Vasicek and the Cox-Ingersol-Ross models. The models were chosen and are widely used because they are tractable and their ease of implementation. The stages of this research activity started by estimating the parameters for the models using Maximum Likelihood Estimation Method. Interest rates were then simulated for the models under study. Next, the reserve value of term insurance policy was determined using the simulated interest rates for the models using the Prospective Method for four randomly generated people of different ages. At the final stage, the results of the reserve values for the models were interpreted and compared. Kenya’s Life Table 2001–2003 was used as the reference in determination of mortality assumptions in reserve calculation. The goodness of fit of the models were done using Likelihood Ratio Test and CIR model was a better fit for the data. Interest rates were highly volatile, a feature replicated better by CIR model. Reserve values were also high for CIR model. Reserve values were higher for male insureds due to a higher mortality rate for men than women while the benefit reserves for the younger age were lower as compared to the older ages.