Valuation of GMWB under stochastic volatility

Abstract

In this paper, we consider the pricing of the variable annuities with Guaranteed Minimum Withdrawal Benefit (GMWB) options, which are deferred, fund-linked annuity contracts, usually with a single premium payment up front. We use the Heston model for the financial market, which assumes the risky asset dynamic follows a stochastic volatility model. The structure of the GMWB policy enables us to adopt the pricing problem of a barrier option. We derive a GMWB pricing partial differential equation (PDE) and the insurance fee is computed by solving an optimization problem. The computed insurance fee is found to be underpriced in the market with a stochastic volatility model. A sensitivity analysis is performed to see the impacts of various parameters on the value of the policy, and the sensitivity of the pricing function with respect to the market risk.

Subject Classification:

• 91G60
• 91G80

Keywords:

• Variable annuity
• GMWB
• Stochastic volatility
• PDE