PRICING PARTICIPATING POLICIES WITH RATE GUARANTEES

We construct the contingent claims models that price participating policies with rate guarantees and default risk. These policies are characterized by the sharing of profits from an investment portfolio between the insurer and the policyholders. A certain reserve distribution mechanism is employed to credit interest at or above certain specified guaranteed rate periodically to the policyholders. Besides the reversionary reserve distribution, terminal bonus is also paid to the policyholders if the terminal surplus is positive. However, the insurer may default at maturity and the policyholders can only receive the residual assets. By neglecting market frictions, mortality risk and surrender option, and under certain assumptions on the interest rate crediting mechanism, we are able to find analytic approximation solution to the pricing model using perturbation techniques. We also develop effective finite difference algorithms for the numerical solution of the contingent claims models. Pricing behaviors of these participating policies with respect to various parameters in the pricing models are examined.