Spectral methods for the calculation of risk measures for variable annuity guaranteed benefits

Runhuan Feng, Hans W. Volkmer

Research output: Contribution to journalArticlepeer-review


Spectral expansion techniques have been extensively exploited for the pricing of exotic options. In this paper, we present novel applications of spectral methods for the quantitative risk management of variable annuity guaranteed benefits such as guaranteed minimum maturity benefits and guaranteed minimum death benefits. The objective is to find efficient and accurate solution methods for the computation of risk measures, which is the key to determining risk-based capital according to regulatory requirements. Our example calculations show that two spectral methods used in this paper are highly efficient and numerically more stable than conventional known methods. Hence these approaches are more suitable for intensive calculations involving death benefits.

Original languageEnglish (US)
Pages (from-to)653-681
Number of pages29
JournalASTIN Bulletin
Issue number3
StatePublished - Sep 2014


  • Asian option
  • Green's function
  • Sturm-Liouville problem
  • Variable annuity guaranteed benefit
  • conditional tail expectation
  • geometric Brownian motion with affine drift
  • risk measures
  • spectral expansion
  • value at risk

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Economics and Econometrics


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