Valuing Contingent Options When The Time-until-death Random Variable Follows Gamma Distribution

In order to enhance competitiveness and reduce business risk, domestic insurance companies developed equity-linked insurance products at the end of last century, such as participating insurance and investment-linked insurance, which met the consumer needs of both obtaining guarantee and gaining investment return. On May11th,2011, China Insurance Regulatory Commission (CIRC) issued two notifications about the commence-ment and management of variable annuities(VAs), which were also equity-linked insurance products. Up to now, there have been three types of variable annuities offered by AXA-Minmetals Assurance Company Limited, MetLife Company and Huatai Life Company Limited in the market. At present, equity-linked insurance products occupy a prevailing position in the American and European countries, while they have a relatively low market share in China. With the further development and maturity of insurance market, they will be popular with more and more consumers in China.Actually, a lot of problems about the pricing of equity-linked insurance products boil down to the valuation of the corresponding embedded contingent options. First, this paper reviews the academic research results on the valuation of the equity-linked contingent options. Second, it introduces the discounted density approach to valuing contingent options in Gerber et al.(2012) and the Jacobi polynomials approximation approach in Dufresne (2007). Next. it values the contingent options using the discounted density approach under the assumption that the time-until-death random variable follows Gamma distribution. In addition, it estimates the value of these options by means of Monte Carlo simulation. At last, the thesis compares the results of the two methods and analyzes the advantages and shortcomings respectively.In the light of the trend of financial market abroad, equity-linked insurance products will become mainstream in China. Therefore, the studies of this paper is of strong practical significance. The main contribution of the thesis is to confirm the results in Gerber(2012) by some numerical examples.