Pricing and insolvency risk evaluating of embedded options in universal insurance considering mortality rate

Focusing on universal life insurance, this paper calculates level premium and constructs the basic model of assets and liabilities considering mortality rate. The model contains interest rate guarantees, surrender options, and mortality rate to fully reflect the reality of prevailing insurance policies. Based on the pricing of universal life insurance, the paper also establishes the insolvency model. Finally, Monte Carlo simulations are conducted to provide numerical results and sensitivity analysis. In order to show the advantages of our model against those without consideration of mortality, we also conducted a mortality scenario test by introducing a mortality modifying factor. Results show that the two embedded derivatives, interest rate guarantee and cancellable option, account for a large proportion in universal insurance's value. This finding may suggest the necessity to consider the interest rate guarantee and cancellable option while assessing the value of the universal insurance, in order to correctly evaluate the solvency of the insurance companies. Results also show that the mortality effect is significant on both embedded option and insolvency risk, which indicates a great necessity of considering mortality in valuation of universal insurance.