Analytical calculation of risk measures for variable annuity guaranteed benefits

Runhuan Feng, Hans W. Volkmer

Research output: Contribution to journalArticlepeer-review


With the increasing complexity of investment options in life insurance, more and more life insurers have adopted stochastic modeling methods for the assessment and management of insurance and financial risks. The most prevalent approach in market practice, Monte Carlo simulation, has been observed to be time consuming and sometimes extremely costly. In this paper we propose alternative analytical methods for the calculation of risk measures for variable annuity guaranteed benefits on a stand-alone basis. The techniques for analytical calculations are based on the study of geometric Brownian motion and its integral. Another novelty of the paper is to propose a quantitative model which assesses both market risk on the liability side and revenue risk on the asset side in the same framework from the viewpoint of risk management. As we demonstrate by numerous examples on quantile risk measure and conditional tail expectation, the methods and numerical algorithms developed in this paper appear to be both accurate and computationally efficient.

Original languageEnglish (US)
Pages (from-to)636-648
Number of pages13
JournalInsurance: Mathematics and Economics
Issue number3
StatePublished - Nov 9 2012
Externally publishedYes


  • Asian option
  • Conditional tail expectation
  • Geometric Brownian motion
  • Hartman-Watson density
  • Integral of geometric Brownian motion
  • Modified Bessel functions
  • Risk measures
  • Value at risk
  • Variable annuity guaranteed benefit

ASJC Scopus subject areas

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


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