Analytical valuation and hedging of variable annuity guaranteed lifetime withdrawal benefits

Research output: Contribution to journalArticlepeer-review


Variable annuity is a retirement planning product that allows policyholders to invest their premiums in equity funds. In addition to the participation in equity investments, the majority of variable annuity products in today's market offer various types of investment guarantees, protecting policyholders from the downside risk of their investments. One of the most popular investment guarantees is known as the guaranteed lifetime withdrawal benefit (GLWB). In current market practice, the development of hedging portfolios for such a product relies heavily on Monte Carlo simulations, as there were no known closed-form formulas available in the existing actuarial literature. In this paper, we show that such analytical solutions can in fact be determined for the risk-neutral valuation and delta-hedging of the plain-vanilla GLWB. As we demonstrate by numerical examples, this approach drastically reduces run time as compared to Monte Carlo simulations. The paper also presents a novel technique of fitting exponential sums to a mortality density function, which is numerically more efficient and accurate than the existing methods in the literature.

Original languageEnglish (US)
Pages (from-to)36-48
Number of pages13
JournalInsurance: Mathematics and Economics
StatePublished - Jan 1 2017


  • Delta-hedging
  • Exponential sums
  • Fitting probability density function
  • Guaranteed lifetime withdrawal benefit
  • Risk-neutral valuation
  • Variable annuity guaranteed benefit

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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