Efficient valuation of a variable annuity contract with a surrender option

We study the partial differential equation (PDE) approach for efficient and accurate valuation of a variable annuity (VA) contract with a surrender option. Specifically, using the Laplace–Carson Transform (LCT), we derive an analytic pricing formula for a VA contract with a surrender option which is formulated as a PDE with an optimal surrender boundary. To demonstrate the efficiency and accuracy of our approach, we show that our pricing formula efficiently provides the exact value of a VA contract. Moreover, we compare the performance of three numerical methods for Laplace inversion to find the most efficient method. Among these methods, we found that the Gaver–Stehfest method is the most efficient pricing for a VA contract with a surrender option.