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 dynamics underlying stock price follow self-exciting switching jump-diffusion process. In this framework, we add jump component to geometric Brownian for large shocks on price. The intensity shock arrivals is Hawkes process modulated by continuous time hidden Markov chain with finite number states. interest rate used discounting stochastic and correlated market. an incomplete market, define equivalent martingale measure variable contract that minimum living or death benefit. Under measure, propose closed-form approximation formulas using inverse Fourier transform technique. A numerical implementation highlights impact jumps economic regimes guarantees.