Pricing Practices for Joint Last Survivor Insurance

In pricing joint last survivor insurance policies, standard industry practice assumes independence of mortality rates among the insured and adds on loading factors to compensate for possible under-estimations of the joint last survivor mortality due to common life style, broken heart factor or common disaster. Considering the fact that the separate mortality experiences for males and females are well documented, we study a dependence relation that describes the joint mortality of married couples in terms of marginal female and male mortality rates. We hope that this will help the insurance industry to utilize the existing single life mortality tables (male / female, smoker / non-smoker, and select / ultimate tables) in pricing joint life policies without relying on the independence assumption and yet reflecting more realistic joint mortality rates. Using data from a large insurance company, we construct a parametric model for the joint survival function based on a Hougaard copula function. The data is from joint annuity contracts and represents mostly married couples. Age difference within a couple is a significant factor in our model. We investigate the association between the marginal survival functions and apply the results to price the joint last survivor insurance using single life tables. 1. Data Analysis The data set is from 14,947 joint and last-survivor annuity contracts of a large Canadian insurer. The contracts were in pay out status over the observation period December 29, 1988 through December 31, 1993. We included 11,457 contracts in our study after eliminating duplicating contracts (3,432) and single sex contracts (58). The fact that the data set reflects lastsurvivor annuities with guarantee periods raises a question of possible under-reporting. Following the insurance industry practice of using integer ages at issue and since we compute discrete insurance premiums y x A , we round the female and male entry ages and termination ages to nearest integer values and denote them as EF , M E , F T and M T . We let D denote the age difference M E EF . The following table is a preliminary data analysis. Table 1. Number of Policies and Observed Deaths by Age Difference D. All Data D<0 D=0 D=1 D=2 D=3 D=4 D>4 Number of Policies (Total) 11457 2133 1037 129