Valuing equity-linked death benefits and other contingent options: A discounted density approach

► The paper presents a discounted probability density function approach to value equity-linked death benefits, such as Guaranteed Minimum Death Benefits in variable annuities. ► Closed-form formulas are obtained for various contingent options, for dynamic fund protection, and for dynamic withdrawal benefits. ► Closed-form formulas are found for the contingent call and put options when there is a fixed expiry date. From these, results for De Moivre's law are obtained as limits. ► The paper also discusses equity-linked death benefit reserves and investment strategies for maintaining such reserves. ► The results in this paper are not restricted to valuing equity-linked benefits payable at the moment of death. The method is applicable to equity-linked benefits payable at the occurrence of a catastrophe and other cases.