Pricing Variable Annuity Contract with GMAB Guarantee Under a Regime Switching Local Volatility Model

This article investigates the pricing of variable annuity guarantees, with particularly emphasising on the Guaranteed Minimum Accumulation Benefit (GMAB) with several embedded options, like roll-up and ratchet. A continuous time model that integrates regime switching dynamics into the local volatility is proposed for the contract’s pricing. As local volatility pioneered by Deelstra and Rayée (2013), on their proposed model by explicitly introducing the regime switching components into the local volatility. Model calibration and valuation are performed through the application of Monte Carlo simulations and Gaussian Process Regression methodologies. For the illustration of the capability of this model and some possible improvements in the model, a numerical and sensitivity analysis is conducted. Uses an empirical test on historical S&P500 Index data to illustrate its practical implications. The results showed that time to maturity, interest rates, and volatilities significantly impact the pricing, and it also illustrates the proposed approach’s accuracy and computational efficiency.