Calculating variable annuity liability "Greeks" using Monte Carlo simulation

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

Research output: Contribution to journalArticle

Abstract

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
Volume45
Issue number2
DOIs
Publication statusPublished - May 2015

Fingerprint

Monte Carlo simulation
Variable annuities
Liability
Estimator
Likelihood ratio
Market risk
Monte Carlo method
Stochastic interest rates
Mixed methods
Finite difference
Risk sensitivity
Stochastic volatility model
Market practices
Hedging strategies
Heston
Interest rates
Equity

Keywords

  • 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

Cite this

Cathcart, Mark J. ; Lok, Hsiao Yen ; McNeil, Alexander J. ; Morrison, Steven. / Calculating variable annuity liability "Greeks" using Monte Carlo simulation. In: ASTIN Bulletin: The Journal of the IAA. 2015 ; Vol. 45, No. 2. pp. 239-266.
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Calculating variable annuity liability "Greeks" using Monte Carlo simulation. / Cathcart, Mark J.; Lok, Hsiao Yen; McNeil, Alexander J.; Morrison, Steven.

In: ASTIN Bulletin: The Journal of the IAA, Vol. 45, No. 2, 05.2015, p. 239-266.

Research output: Contribution to journalArticle

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