This article investigates the valuation of annuity guarantees under a regime-switching model when the dynamics of the underlying stock price follow a self-exciting switching jump-diffusion process. In this framework, we add a jump component to a regime-switching geometric Brownian for large shocks on the stock price. The intensity of shock arrivals is a Hawkes process modulated by a continuous time hidden Markov chain with a finite number of states. The interest rate used for discounting is stochastic and correlated to the stock market. In an incomplete market, we define an equivalent martingale measure to price a variable annuity contract that guarantees a minimum living or death benefit. 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.

本文研究了当基础股票价格的动态遵循自激转换跳跃扩散过程时，在制度转换模型下的年金担保估值。在这个框架中，我们将一个跳跃分量添加到一个状态转换几何布朗方程中，以应对股价的巨大冲击。冲击波的强度是一个霍克斯过程，由具有有限个状态的连续时间隐马尔可夫链调制。用于贴现的利率是随机的并且与股票市场相关。在不完全市场中，我们定义了一个等价的鞅测度来为保证最低生活或死亡抚恤金的可变年金合同定价。在这个等价的鞅测度下，我们提出了使用傅里叶逆变换技术的封闭式逼近公式。