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.

Asset-liability management, C-3 Risk, Loss Reserves, Surplus, Stochastic models, Deterministic Models

1. Actuarial Education Company (2013) Study materials. [Google Scholar] [Crossref]

2. Barber, J.R., and Copper, M.L.” Is Bond Convexity a Free Lunch?” The Journal of Portfolio Management, Fall 1997: 113-119. [Google Scholar] [Crossref]

3. Bellhouse, D.R., and Panjer, H.H.” Stochastic Modeling of Interest Rates with Applications to Life Contingencies-Part II.” Journal of Risk and Insurance 48 (1992): 275-287. [Google Scholar] [Crossref]

4. Black. F.’ &’ Scholes. M. The Pricing of Options and Corporate Liabilities. Journal of Political Economy,81(3), 637-654.doi:10.1086/260062. (1973) [Google Scholar] [Crossref]

5. Brown B. Z. Considerations in setting loss reserves. Casualty Loss reserve seminar, retrieved (1988) [Google Scholar] [Crossref]

6. Chan, K.C., Karolyi, GA, Long staff, FA, and Sanders, A.B.” An Empirical Comparison of Alternative Models of the Short-Term Interest Rate.” The Journal of Finance 47 (1992): 1209-1227. [Google Scholar] [Crossref]

7. Christensen, P.O., and Sorensen, B.G.” Duration, Convexity, and Time Value.” The Journal of Portfolio Management, Winter 1994:51-60. [Google Scholar] [Crossref]

8. Cox, J. c., Ingersoll,]. E. and Ross, SA ”A Re-Examination of Traditional Hypotheses About the Term Structure of Interest Rates.” The Journal of Finance 36 (1981): 769-799.35 [Google Scholar] [Crossref]

9. Cox, lC., Ingersoll, lE. and Ross, S.A.” A Theory of the Term Structure of Interest Rates.” Econometrica 53 (1985): 385-407. [Google Scholar] [Crossref]

10. Dothan, L.U.” On the Term Structure of Interest Rates.” Journal of Financial Economics 6 (1977): 59-69. [Google Scholar] [Crossref]

11. Douglas, L.G. Bond Risk Analysis: A Guide to Duration and Convexity New York, N.Y.: New York Institute of Finance, 1990. [Google Scholar] [Crossref]

12. Tzeng, L.Y., Wang, J.L. and Soo, J.” Surplus Management Under a Stochastic Process.” Journal of Risk and Insurance 67 (2000): 451-462. [Google Scholar] [Crossref]

• Cyberverse: A Game-Based Learning Application for Cyber Security
• Design and Development of a Low Cost Smart Electronic School Bell
• Assessing the Effectiveness of TVET Training in Enhancing Youth Employability: A Case Study of Kisumu County, Kenya
• Social Penetration Analysis in Self-Disclosure of Online Loan Application Users to Their Partners
• Optimization of Maintenance Strategies in an Oil and Gas Production Facility to Minimize Maintenance Cost