Efficient valuation of variable annuities under regime-switching jump diffusion models with surrender risk and mortality risk

We present an efficient valuation approach for guaranteed minimum accumulation benefits (GMABs), guaranteed minimum death benefits (GMDBs), and surrender benefits (SBs) embedded in variable annuity (VA) contracts in a regime-switching jump diffusion model. We incorporate into the contract the risks of mortality and surrender, with these events generally monitored discretely over the life of the policy. Using a combination of the continuous-time Markov chain (CTMC) approximation and the Fourier cosine series expansion (COS) method, we determine that the valuation problem can be resolved within a regime-switching jump diffusion framework. Extensive numerical experiments showcase the efficiency of the proposed method, which proves to be more advantageous when compared to existing approaches like Monte Carlo (MC) simulation. The thorough analysis explores how model parameters affect the valuation outcomes.