Abstract
Variable annuities are often sold with guarantees to protect investors from downside investment risk. The majority of variable annuity guarantees are written on more than one asset, but in practice, single-asset (univariate) stochastic investment models are mostly used for pricing and hedging these guarantees. This practical shortcut may lead to problems such as basis risk. In this article, we contribute a multivariate framework for pricing and hedging variable annuity guarantees. We explain how to transform multivariate stochastic investment models into their risk-neutral counterparts, which can then be used for pricing purposes. We also demonstrate how dynamic hedging can be implemented in a multivariate framework and how the potential hedging error can be quantified by stochastic simulations.
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