Joint-life Variable Annuity Insurance Design And Valuation

Since the50s of20th century, variable annuity has become quite popular in North America insurance markets. After sixty years, the techniques for product invention, pricing and risk management are much maturer and accordingly, the market super-vision system is continuously improved. Variable annuity insurance with minimum guarantees, as one kind of the investment-linked insurance, not only protects policy holders from death and survival risk but also entitles policy holders to profit from investment benefit of financial market, which is able to beat against inflation leading to depreciation of purchase power. As a result, the demand for variable annuity is increasing rapidly. Insurance market in China is young but vigorous. The consumers' requirements for diversity and flexibility are raising. In2011, China Insurance Reg-ulatory Commission permits eight companies to sell variable annuity with minimum guarantees. It shows variable annuity insurance is officially introduced to China.Based on individual variable annuity and joint-life annuity design, this paper intends to propose three types of joint-life variable annuity insurance embedded with certain guaranteed benefit options. According to clauses stated in insurance policy and techniques used in valuing single-life variable annuity, this paper provides theoretical actuarial models, which are based on classical financial assumptions, to price these joint-life variable annuity respectively. During pricing process, in order to make the contract price reasonable and accurate, different from the formal practice that assuming couples' life are independent from each other, this paper considers the dependency between two related life and applies Copula function to combine two marginal distribution as one to demonstrate wife-and-husband joint longevity structure. Afterwards, methods of simulation are used to compare the contract value under assumption of dependent and independent situation. Lastly, regarding of risks, this paper is concluded with remarks and suggestions to promote sales of the newly designed products.