Pricing of GMWB Options in Variable Annuities under Stochastic Volatility, Stochastic Interest Rates and Stochastic Mortality via the Componentwise Splitting Method

Nikolay Gudkov, Katja Ignatieva and Jonathan Ziveyi

This paper values Guaranteed Minimum Withdrawal Benefit (GMWB) riders embedded in variable annuities assuming that the underlying fund dynamics evolve under the influence of stochastic interest rates, stochastic volatility, stochastic mortality and equity risk. The valuation problem is formulated as a partial differential equation (PDE) which is solved numerically by employing the operator splitting method.