The standard market risk model of the Swiss solvency test: an analytic solution

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, 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.