With the commencement of the Solvency II directive, insurers in the European Union need to provide a projection of their solvency figures into the future (as part of the Own Risk and Solvency Assessment, ORSA). This is a highly complex task since future solvency figures depend on the development of numerous (stochastic) risk factors. The required evaluations are numerically challenging, which in practice forces companies to limit their analyses to only a few selected deterministic scenarios. These deterministic scenarios clearly cannot describe the full probability distribution of a company’s future solvency situation. The focus of this paper is on financial guarantees in participating life insurance products. In particular, we study two major types of interest rate guarantees in life insurance, a maturity guarantee and a (path-dependent) cliquet-style guarantee. In order to derive entire probability distributions of future solvency ratios, we limit the model framework to two sources of risk (a Hull–White model for interest rates and a geometric Brownian motion for stocks). This partly leads to closed-form solutions of the market-consistent valuation of the liabilities, ensures higher accuracy in computations and less numerical effort. Furthermore, the model allows for a detailed analysis of the impact of the different types of interest rate guarantees on the future solvency situation. Our results suggest that the type of guarantee has a significant impact on the long-term solvency of the company.

随着Solvency II指令的实施，欧盟的保险公司需要提供其未来偿付能力数字的预测（作为ORSA自身风险和偿付能力评估的一部分）。这是一项非常复杂的任务，因为未来的偿付能力数字取决于众多（随机）风险因素的发展。所需的评估在数值上具有挑战性，实际上迫使公司将其分析限制在仅少数几个确定性方案中。这些确定性场景显然无法描述公司未来偿付能力状况的全部概率分布。本文的重点是参与人寿保险产品的财务担保。特别是，我们研究了寿险中两种主要的利率担保，成熟度保证和（依赖路径的）攀爬风格保证。为了得出未来偿付能力比率的全部概率分布，我们将模型框架限制为两种风险来源（利率为赫尔-怀特模型，股票为几何布朗运动）。这部分导致了市场一致的债务估值的封闭式解决方案，确保了计算的更高准确性和更少的数值工作。此外，该模型允许对不同类型的利率担保对未来偿付能力状况的影响进行详细分析。我们的结果表明，担保的类型对公司的长期偿付能力有重大影响。我们将模型框架限制为两种风险来源（用于利率的赫尔-怀特模型和用于股票的几何布朗运动）。这部分导致了市场一致的债务估值的封闭式解决方案，确保了计算的更高准确性和更少的数值工作。此外，该模型允许对不同类型的利率担保对未来偿付能力状况的影响进行详细分析。我们的结果表明，担保的类型对公司的长期偿付能力有重大影响。我们将模型框架限制为两种风险来源（用于利率的赫尔-怀特模型和用于股票的几何布朗运动）。这部分导致了市场一致的债务估值的封闭式解决方案，确保了计算的更高准确性和更少的数值工作。此外，该模型允许对不同类型的利率担保对未来偿付能力状况的影响进行详细分析。我们的结果表明，担保的类型对公司的长期偿付能力有重大影响。该模型允许对不同类型的利率担保对未来偿付能力状况的影响进行详细分析。我们的结果表明，担保的类型对公司的长期偿付能力有重大影响。该模型允许对不同类型的利率担保对未来偿付能力状况的影响进行详细分析。我们的结果表明，担保的类型对公司的长期偿付能力有重大影响。