European Actuarial Journal最新文献

The Rough Fractional Stochastic Volatility (RFSV) model of Gatheral et al. (Quant Financ 18(6):933-949, 2014) is remarkably consistent with financial time series of past volatility data as well as with the observed implied volatility surface. Two tractable implementations are derived from the RFSV with the rBergomi model of Bayer et al. (Quant Financ 16(6):887-904, 2016) and the rough Heston model of El Euch et al. (Risk 84-89, 2019). We now show practically how to expand these two rough volatility models at larger time scales, we analyze their implications for the pricing of long-term life insurance contracts and we explain why they provide a more accurate fair value of such long-term contacts. In particular, we highlight and study the long-term properties of these two rough volatility models and compare them with standard stochastic volatility models such as the Heston and Bates models. For the rough Heston, we manage to build a highly consistent calibration and pricing methodology based on a stable regime for the volatility at large maturity. This ensures a reasonable behavior of the model in the long run. Concerning the rBergomi, we show that this model does not exhibit a realistic long-term volatility with extremely large swings at large time scales. We also show that this rBergomi is not fast enough for calibration purposes, unlike the rough Heston which is highly tractable. Compared to standard stochastic volatility models, the rough Heston hence provides efficiently a more accurate fair value of long-term life insurance contracts embedding path-dependent options while being highly consistent with historical and risk-neutral data.

In a run-off triangle external factors can have a similar influence on all incremental losses of the same calendar year. This can distort the triangle such that reserving methods like chain ladder or the loss ratio method do not work properly. A very recent example of such an external factor is the Covid-19 pandemic. In many countries, the insurance industry is in the process of establishing market knowledge about the impact of the pandemic on premiums and losses. We extend the additive claims reserving model to allow for calendar year effects and develop a variant of the incremental loss ratio method (also known as the additive method) that can make use of such market knowledge. We derive formulas for the mean squared error of prediction and provide a detailed numerical example.

Supplementary information: The online version contains supplementary material available at 10.1007/s13385-022-00315-3.

Predicting the number of outstanding claims (IBNR) is a central problem in actuarial loss reserving. Classical approaches like the Chain Ladder method rely on aggregating the available data in form of loss triangles, thereby wasting potentially useful additional claims information. A new approach based on a micro-level model for reporting delays involving neural networks is proposed. It is shown by extensive simulation experiments and an application to a large-scale real data set involving motor legal insurance claims that the new approach provides more accurate predictions in case of non-homogeneous portfolios.

Supplementary information: The online version contains supplementary material available at 10.1007/s13385-022-00314-4.

This paper proposes a spline mortality model for generating smooth projections of mortality improvement rates. In particular, we follow the two-dimensional cubic B-spline approach developed by Currie et al. (Stat Model 4(4):279-298, 2004), and adopt the Bayesian estimation and LASSO penalty to overcome the limitations of spline models in forecasting mortality rates. The resulting Bayesian spline model not only provides measures of stochastic and parameter uncertainties, but also allows external opinions on future mortality to be consistently incorporated. The mortality improvement rates projected by the proposed model are smoothly transitioned from the historical values with short-term trends shown in recent observations to the long-term terminal rates suggested by external opinions. Our technical work is complemented by numerical illustrations that use real mortality data and external rates to showcase the features of the proposed model.