Valuing Variable Annuity Guarantees on Multiple Assets

Scandinavian Actuarial Journal, 2015, DOI:10.1080/03461238.2015.1102167

Posted: 25 Nov 2015

See all articles by Jonathan Ziveyi

Jonathan Ziveyi

UNSW Australia

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Date Written: October 30, 2015


Guarantees embedded variable annuity contracts exhibit option-like payoff features and the pricing of such instruments naturally leads to risk neutral valuation techniques. This paper considers the pricing of two types of guarantees; namely, the Guaranteed Minimum Maturity Benefit and the Guaranteed Minimum Death Benefit riders written on several underlying assets whose dynamics are given by affine stochastic processes. Within the standard affine framework for the underlying mortality risk, stochastic volatility and correlation risk, we develop the key ingredients to perform the pricing of such guarantees. The model implies that the corresponding characteristic function for the state variables admits a closed form expression. We illustrate the methodology for two possible payoffs for the guarantees leading to prices that can be obtained through numerical integration. Using typical values for the parameters, an implementation of the model is provided and underlines the significant impact of the assets’ correlation structure on the guarantee prices.

Keywords: mortality risk, variable annuity, stochastic volatility risk, correlation risk, multiple assets, European option

JEL Classification: C63, G22, G13, G12

Suggested Citation

Ziveyi, Jonathan and Da Fonseca, José, Valuing Variable Annuity Guarantees on Multiple Assets (October 30, 2015). Scandinavian Actuarial Journal, 2015, DOI:10.1080/03461238.2015.1102167. Available at SSRN:

Jonathan Ziveyi

UNSW Australia ( email )

School of Risk and Actuarial Studies
Level 6 East Wing, Business School
Sydney, NSW 2052
+61 2 9385 8006 (Phone)
+61 2 9385 1883 (Fax)

José Da Fonseca (Contact Author)

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

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