We present an efficient valuation approach for guaranteed minimum benefits embedded in variable annuity contracts, where the log price follows a jump-diffusion model with stochastic volatilities. In particular, we allow separate Cox-Ingersoll-Ross processes for the underlying volatility and the jump intensity, each correlated with the diffusion term of the spot price. To value the contract under such complex stochastic nature, we rely on the recent advances in the frame dual projection methods with the stochastic process approximated by its expectation. As a byproduct of the transparent analytical expression derived, we derive the associated Greeks that provide a practical basis for risk management. Numerical experiments demonstrate the accuracy and efficiency of the proposed method.

我们为可变年金合同中嵌入的保证最低收益提出了一种有效的估值方法，其中对数价格遵循具有随机波动性的跳跃扩散模型。特别是，我们允许对基础波动率和跳跃强度进行单独的 Cox-Ingersoll-Ross 过程，每个过程都与现货价格的扩散项相关。为了在这种复杂的随机性质下对合约进行估值，我们依靠框架双投影方法的最新进展，其随机过程近似于其期望。作为导出的透明分析表达式的副产品，我们导出了相关的希腊字母，为风险管理提供了实用的基础。数值实验证明了该方法的准确性和效率。