This paper proposes a new model, the linear-rational Wishart model, which allows the joint modelling of mortality and interest rate risks. Within this framework, we obtain closed-form solutions for the survival bond and the survival floating rate bond. We also derive a closed-form solution for the guaranteed annuity option, i.e., an option on a sum of survival (floating rate) bonds, which can be computed explicitly up to a one-dimensional numerical integration, independent of the model dimension. Using realistic parameter values, we provide a model implementation for these complex derivatives that illustrates the flexibility and efficiency of the linear-rational Wishart model.

本文提出了一种新模型，即线性有理 Wishart 模型，该模型允许对死亡率和利率风险进行联合建模。在此框架内，我们获得了生存债券和生存浮动利率债券的封闭式解。我们还得出了保证年金期权的封闭式解，即生存（浮动利率）债券总和的期权，它可以明确地计算到一维数值积分，与模型维度无关。使用实际的参数值，我们为这些复杂的导数提供了一个模型实现，说明了线性有理 Wishart 模型的灵活性和效率。