Spectral Methods For The Calculation Of Risk Measures For Variable Annuity Guaranteed Benefits

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.