Incorporating Longevity Risk and Medical Information into Life Settlement Pricing

A life settlement is a financial transaction in which the owner of a life insurance policy sells her policy to a third party. We present an overview of the life settlement market, exhibit its susceptibility to longevity risk, and discuss it as part of a new asset class of longevity related securities. We discuss pricing where the investor has information concerning the expected life expectancy of the insured as well as perhaps other medical information obtained from a medical underwriter. We show how to incorporate this information into the investor's valuation in a rigorous and statistically justified manner. To incorporate medical information, we apply statistical information theory to adjust a pre-specified standard mortality table so as to obtain a new mortality table that exactly reflects the known medical information. We illustrate using several mortality tables including a new extension of the Lee-Carter model that allows for jumps in mortality and longevity over time. The information theoretically adjusted mortality table has a distribution consistent with the underwriter's projected life expectancy or other medical underwriter information and is as indistinguishable as possible from the pre-specified mortality model. An analysis using several different potential standard tables and medical information sets illustrates the robustness and versatility of the method.