In this article, we derive a closed-form pricing formula for catastrophe equity put options under a stochastic interest rate framework. A distinguishing feature of the proposed solution is its simplified form in contrast to several recently published formulae that require evaluating several layers of infinite sums of $n$-fold convoluted distribution functions. As an application of the proposed formula, we consider two different frameworks and obtain the closed-form formula for the joint characteristic function of the asset price and the losses, which is the only required ingredient in our pricing formula. The prices obtained by the newly derived formula are compared with those obtained using Monte-Carlo simulations to show the accuracy of our formula.

在本文中，我们推导出了随机利率框架下巨灾股票看跌期权的封闭式定价公式。所提出的解决方案的一个显着特征是它的简化形式，与最近发布的几个公式相比，这些公式需要评估几层无限和的$n$ -fold 卷积分布函数。作为所提出公式的应用，我们考虑了两个不同的框架，并获得了资产价格和损失的联合特征函数的封闭式公式，这是我们定价公式中唯一需要的成分。将新推导出的公式获得的价格与使用蒙特卡罗模拟获得的价格进行比较，以显示我们公式的准确性。