Pricing Variable Annuity Guarantees in a Local Volatility Framework

39 Pages Posted: 4 Apr 2012

See all articles by Grégory Rayée

Grégory Rayée

Université Libre de Bruxelles (ULB)

Griselda Deelstra

Université Libre de Bruxelles (ULB)

Date Written: April 3, 2012


In this paper, we study the price of Variable Annuity Guarantees, especially of Guaranteed Annuity Options (GAO) and Guaranteed Minimum Income Benefit (GMIB), and this in the settings of a derivative pricing model where the underlying spot (the fund) is locally governed by a geometric Brownian motion with local volatility, while interest rates follow a Hull-White one-factor Gaussian model. Notwithstanding the fact that in this framework, the local volatility depends on a particularly complicated expectation where no closed-form expression exists and it is neither directly related to European call prices or other liquid products, we present in this contribution different methods to calibrate the local volatility model. We further compare Variable Annuity Guarantee prices obtained in three different settings, namely the local volatility, the stochastic volatility and the constant volatility models all combined with stochastic interest rates and show that an appropriate volatility modelling is important for these long-dated derivatives. More precisely, we compare prices of GAO, GMIB Rider and barrier types GAO obtained by using local volatility, stochastic volatility and constant volatility models.

Keywords: local volatility, stochastic interest rates, variable annuity guarantees, GAO, GMIB

Suggested Citation

Rayée, Grégory and Deelstra, Griselda, Pricing Variable Annuity Guarantees in a Local Volatility Framework (April 3, 2012). Available at SSRN: or

Grégory Rayée (Contact Author)

Université Libre de Bruxelles (ULB) ( email )

CP 114/04 Av FD Roosevelt 50
Brussels, 1050

Griselda Deelstra

Université Libre de Bruxelles (ULB) ( email )

Boulevard du Triomphe, CP210
Brussels, Brussels 1050

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics