Valuing variable annuity guarantees with the multivariate Esscher transform

Andrew Cheuk-Yin Ng and Johnny Siu-Hang Li

Insurance: Mathematics and Economics, 2011, vol. 49, issue 3, 393-400

Abstract: Variable annuities are usually sold with a range of guarantees that protect annuity holders from some downside market risk. Although it is common to see variable annuity guarantees written on multiple funds, existing pricing methods are, by and large, based on stochastic processes for one single asset only. In this article, we fill this gap by developing a multivariate valuation framework. First, we consider a multivariate regime-switching model for modeling returns on various assets at the same time. We then identify a risk-neutral probability measure for use with the model under consideration. This is accomplished by a multivariate extension of the regime-switching conditional Esscher transform. We further extend our results to the situation when the guarantee being valued is linked to equity indexes measured in foreign currencies. In particular, we derive a probability measure that is risk-neutral from the perspective of domestic investors. Finally, we illustrate our results with a hypothetical variable annuity guarantee.

Keywords: Minimum entropy; Incomplete market; Quanto; Regime-switching (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (20)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:49:y:2011:i:3:p:393-400

DOI: 10.1016/j.insmatheco.2011.06.003

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