An FFT Approach to Price Guaranteed Minimum Death Benefit in Variable Annuities under a Regime-Switching Model

This paper considers the valuation of guaranteed minimum death benefit in variable annuities under a regime-switching model. More specifically, the risk-free interest rate, the appreciation rate and the volatility of the reference investment fund are modulated by a continuous-time, finite-state, observable Markov chain. A regime-switching Esscher transform is adopted to select an equivalent martingale measure in the incomplete financial market. Inverse Fourier transform is used to derive an analytical pricing formula for the embedded option in variable annuity with guaranteed minimum death benefit. To calculate the fair guarantee charge, fast Fourier transform approach is applied. Numerical examples are provided to illustrate the practical implementation and the relationship between the fair guarantee charges and other parameters.