Modeling the Premium and Contract Properties of Family Takaful (Islamic Life Insurance)

The premium is a deterministic function to compensate for losses due to random events, and a crucial element for the operation of the standard insurance company. This paper focuses on the practice of family takāful and considers properties of the contract in determining the premiums comprehensively and in a way that makes them Sharīʿah-compliant. We have developed a new mortality derivative formula and model of the premium for an equity-linked policy (unit-linked product). We have adapted the option pricing of the Black-Scholes model for periodical premiums, taking into account a minimum death benefit, the value of surrender option, and maturity guaranteed payoff. We have also added some assumptions for the underlying asset prices following negative discrete dividend extensions from the dynamic escrowed model. The purpose is to obtain an unbiased option price for the underlying asset. We found it to be a satisfying product with a fair periodical premium, which has great flexibility in its features and complies comprehensively with Sharīʿah law