Abstract

Equity-indexed annuity (EIA) insurance products have become increasingly sought after since their introduction in 1995. Some of the most important characteristics of these products are that they allow the policyholders to benefit from the equity market's potential growth and ensure that the principals can grow with a minimum guaranteed interest rate. In this thesis, we show how to derive the closed-form pricing formula of a point-to-point financial guarantee, using the Black-Scholes framework. Moreover, under the complete-market assumption, we construct a replicating portfolio that can hedge a point-to-point financial guarantee. However, in real financial markets, some of the assumptions required by a complete-market cannot be respected, particularly the continuous-time trading assumption. The replicating portfolio generates hedging errors because companies can only trade discretely. We will show the distribution of the present values of hedging errors for the financial guarantee. We also introduce the Lee-Carter stochastic mortality model. After presenting how to price a point-to-point equity-indexed annuity with fixed mortality rates, we then take the stochastic mortality rates into consideration to re-evaluate the point-to-point. In both cases, the pricing work for the point-to-point product is done under the assumption of independence between the equity market and the policyholder's time of death. Furthermore, the replicating portfolio of a point-to-point equity-indexed annuity can be derived based on the replicating portfolio of a point-to-point financial guarantee with the corresponding mortality rates. The distributions of the present values of hedging errors under both fixed and stochastic mortality rates will be presented. Indeed, the replicating portfolio can help companies reduce the risks of issuing EIA products, since it can hedge the EIA very well. The impact of stochastic mortality model is examined at the end of the thesis