Valuation of Annuity Guarantees under a Self-Exciting Switching Jump Model

This article investigates the valuation of annuity guarantees under a regime-switching model when the dynamics of the underlying stock price follows a self-exciting switching jump diffusion process. In this framework, the intensity of shock arrivals, the return and volatility of shocks are modulated by a continuous time hidden Markov chain with a finite number of states. The interest rate is stochastic and correlated to the stock market. In an incomplete market, we define an equivalent martingale measure to price a variable annuity contract with a minimum guarantee in case of death or life. Under this equivalent martingale measure, we propose closed-form approximation formulas using the inverse Fourier transform technique. A numerical implementation highlights the impact of self-exciting jumps and economic regimes on the valuation of guarantees.