Pricing of Guaranteed Annuity Options in a Stochastic Volatility and Interest Rate Environment

Abstract

Abstract This article examines the pricing of guaranteed annuity options (GAOs) in a stochastic volatility and interest rate model. While the pricing of these options in a stochastic volatility and interest rate model has been examined in van Haastrecht, Plat, and Pelsser (2010. Insurance: Mathematics and Economics 47:266–77), the pricing is difficult under the general stochastic volatility environment. In order to overcome these difficulties, we examined the asymptotic expansion method introduced by Kim and Kunitomo (1999. Asia-Pacific Financial Markets 6:49–70) and extended by Kim (2002. Journal of the Operations Research Society of Japan 45:404–25), and Kunitomo and Kim (2007. Japanese Economic Review 58:71–106). The asymptotic expansion method obtains a closed-form approximation formula for the price of GAOs in a general stochastic volatility environment including the Schöbel–Zhu–Hull–White model and the Heston–Hull–White model, for example. We confirm the accuracy of the asymptotic expansion methods by numerical demonstrations. The sensitivity analysis of the options price to changes in the parameters for the stochastic volatility process is also analyzed.