Calculating variable annuity liability "Greeks" using Monte Carlo simulation

Mark J. Cathcart, Hsiao Yen Lok, Alexander J. McNeil*, Steven Morrison

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a "bump and revalue" method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators should be preferred. This paper considers a stylized guaranteed minimum withdrawal benefit product in which the reference equity index follows a Heston stochastic volatility model in a stochastic interest rate environment. The complete set of first-order sensitivities with respect to index value, volatility and interest rate and the most important second-order sensitivities are calculated using PW, likelihood-ratio and mixed methods. It is observed that the PW method delivers the best estimates of first-order sensitivities while mixed estimation methods deliver considerably more accurate estimates of second-order sensitivities; moreover there are significant computational gains involved in using PW and mixed estimators rather than simple BnR estimators when many Greeks have to be calculated.

Original languageEnglish
Pages (from-to)239-266
Number of pages28
JournalASTIN Bulletin: The Journal of the IAA
Issue number2
Publication statusPublished - May 2015


  • Greeks
  • Heston stochastic volatility model
  • likelihood-ratio method
  • Monte Carlo estimation
  • pathwise method
  • sensitivities
  • stochastic interest rates
  • Stochastic simulation
  • variable annuity

ASJC Scopus subject areas

  • Finance
  • Accounting
  • Economics and Econometrics


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