The full standard model of the Swiss solvency test (SST) requires a Monte Carlo simulation to calculate the regulatory target capital. This paper derives an alternative fast Fourier transform-based computational approach for calculating the target capital of the SST that is more than 600 times faster than a Monte Carlo simulation. We also show that the relative computational error of our approach is much smaller than that of the saddlepoint approximation method: the error of the former is less than 10-8, whereas the error of the latter can be as large as 24% for the numerical examples we consider. Our algorithm is relevant for applications requiring both speed and precision, such as multiperiod SST analysis, portfolio optimization and, more generally, the various economic asset and liability management applications of non-Swiss insurers, for which the expected shortfall of asset and liability fluctuations needs to be calculated in a fast and accurate way.

中文翻译：

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瑞士偿付能力测试的标准市场风险模型：解析解

瑞士偿付能力测试 (SST) 的完整标准模型需要蒙特卡罗模拟来计算监管目标资本。本文推导出一种替代的基于快速傅立叶变换的计算方法，用于计算 SST 的目标资本，其速度比蒙特卡罗模拟快 600 多倍。我们还表明，我们的方法的相对计算误差远小于鞍点近似方法：前者的误差小于 10-8，而后者的误差可高达 24% 的数值我们考虑的例子。我们的算法适用于需要速度和精度的应用程序，例如多周期 SST 分析、投资组合优化，以及更一般地说，非瑞士保险公司的各种经济资产和负债管理应用程序，