On the variability of return periods of European winter precipitation extremes over the last three centuries

We investigate the changes of extreme European winter (December-February) precipitation back to 1700 and show for various European regions that return periods of extremely wet and dry winters are subject to significant changes both before and after the onset of anthropogenic influences. Generally, winter precipitation has become more extreme. We also examine the spatial pattern of the changes of the extremes covering the last 300 years where data quality is sufficient. Over central and Eastern Europe dry winters occurred more frequently during the 18th and the second part of the 19th century relative to 1951–2000. Dry winters were less frequent during both the 18th and 19th century over the British Isles and the Mediterranean. Wet winters have been less abundant during the last three centuries compared to 1951–2000 except during the early 18th century in central Europe. Although winter precipitation extremes are affected by climate change, no obvious connection of these changes was found to solar, volcanic or anthropogenic forcing. However, physically meaningful interpretation with atmospheric circulation changes was possible.

The Risk Management of Minimum Return Guarantees

Contracts paying a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specified relative to a benchmark portfolio, are closely related to unit-linked life-insurance products and can be considered as alternatives to direct investment in the underlying benchmark. They contain an embedded power option, and the key issue is the tractable and realistic hedging of this option, in order to rigorously justify valuation by arbitrage arguments and prevent the guarantees from becoming uncontrollable liabilities to the issuer. We show how to determine the contract parameters conservatively and implement robust risk-management strategies.

Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.