Pricing Guaranteed Minimum Death Benefit Contracts under the Phase-Type Law of Mortality

摘要

Under the assumption that the time to death random variable follows a phase-type distribution, we study the pricing of two types of guaranteed minimum death benefit contracts: (i) GMDB with roll-up feature and (ii) GMDB with a fixed guarantee level. Within the Black-Scholes option pricing framework, we attempt to derive matrix-analytic formulas for the GMDB price and the total expenses. We also discuss an alternative Monte-Carlo method for practical applications.