Risk Analysis of Life Insurance Products

This paper takes a simple life insurance product that pays a benefit upon the death of a person and looks at two separate ways of setting the price, or premium, for the product. The premium is collected only once; on the date that the product is purchased. The first method of pricing uses the actuarial present value of the insurance product to set the single premium. On average, when pricing at the actuarial present value the person selling the product will break even on gains and losses. However, in individual cases there is the risk of large losses that the seller cannot control when pricing at the actuarial present value.The second method of pricing allows the person setting the premium to have more control over losses by looking at the value at risk. Under the value at risk method, the price charged guarantees that the seller will not lose more than a certain amount of money with a set confidence level. Both pricing methods are analyzed first under a constant rate of return and then later using a yield curve of varying interest rates.Finally, this paper looks at how changing the rates of return from constant rates to varying rates affect the amount of money that the seller has on hand to pay benefits under both pricing methods. It is determined that the appropriate method to use in pricing the product depends upon the sellers market competition for similar products and the level of risk the seller is willing to undertake.