Pricing participating policies with rate guarantees and bonuses
نویسندگان
چکیده
We construct the contingent claims models that price participating policies with rate guarantees, bonuses and default risk. These policies are characterized by the sharing of profits from an investment portfolio between the insurer and the policy holders. A certain surplus distribution mechanism (reversionary bonus) is employed to credit interest at or above certain specified guaranteed rate periodically to the policy holders. Besides the reversionary bonus, terminal bonus is also paid to the policy holder if the terminal surplus is positive. However, the insurer may default at maturity and the policy holders can only receive the residual assets. By neglecting market frictions, mortality risk and surrender option, and under certain assumptions on the bonus distribution mechanism, we are able to find analytic approximation solution to the pricing model. 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.
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