In this paper we deal with a variable annuity which provides guarantees at death and maturity financed through the application of a state-dependent fee structure of the threshold type. Our first aim is to test the use of least squares Monte Carlo methods (LSMC) for the numerical implementation of the valuation model. In fact, special care is needed when applying LSMC, due to the shape of the surrender region. To this end we introduce a quite general framework, under which we derive a theoretical result that allows us to stem the numerical errors arising in the regression step of the valuation algorithm. The second aim of the paper is to analyse numerically the interaction between the various contract components, in particular fee rates/thresholds and surrender penalties, under alternative policyholder behaviours. This analysis turns out to be very useful, in particular when addressing the problem of the contract design.

中文翻译：

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带有阈值费用的可变年金：估值，数值实现和比较静态分析

在本文中，我们处理可变年金，该年金通过使用阈值类型的国家相关费用结构提供死亡和成熟期担保。我们的首要目标是测试最小二乘蒙特卡罗方法（LSMC）在估值模型的数值实现中的使用。实际上，由于交出区域的形状，在应用LSMC时需要特别小心。为此，我们引入了一个非常通用的框架，在该框架下，我们得出了一个理论结果，该理论结果使我们能够阻止在估值算法的回归步骤中出现的数值误差。本文的第二个目的是在替代保单持有人的行为下，数字分析各种合同组成部分之间的相互作用，特别是费率/门槛和退保罚款。