| Summary: | 碩士 === 東吳大學 === 商用數學系 === 96 === Guaranteed minimum withdrawal benefit (GMWB) is a very popular rider on variable annuities (VA). It promises annuitants to earn the entire initial investment, regardless of investment performance, yet spread over an established time period.
In this paper, we extend the “static model” in Milevsky and Salisbury (2006) by considering a more realistic situation that VA could lapse during the guaranteed period if the annuitant dies earlier. And if this happens, remaining annuity payments discontinue, whereas a death benefit will be offered to maintain the minimum withdrawal guarantee. Two different death benefits are considered including the market value of the separate account at the annuitant’s death; and the greater of the withdrawal account and the market value of the separate account mentioned above. We decompose the GMWB with death benefits into a certain-year temporary life annuity plus a Quanto Asian put with random maturity date; and then explore their values. Finally, in order to sustain the insurer’s capacity to absorb the downside financial risk and the systematic risk, appropriate a proportional fee under the fair price and risk-neutral framework is evaluated numerically via Monte Carlo simulation, moreover, financial risk measure is evaluated by the same way.
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