An appropriate calibration and forecasting of volatility and market risk are some of the main challenges faced by companies that have to manage the uncertainty inherent to their investments or funding operations such as banks, pension funds or insurance companies. This has become even more evident after the 2007-2008 Financial Crisis, when the forecasting models assessing the market risk and volatility failed. Since then, a significant number of theoretical developments and methodologies have appeared to improve the accuracy of the volatility forecasts and market risk assessments. Following this line of thinking, this paper introduces a model based on using a set of Machine Learning techniques, such as Gradient Descent Boosting, Random Forest, Support Vector Machine and Artificial Neural Network, where those algorithms are stacked to predict S&P500 volatility. The results suggest that our construction outperforms other habitual models on the ability to forecast the level of volatility, leading to a more accurate assessment of the market risk.

Events such as the Financial Crisis of 2007–2008 or the COVID-19 pandemic caused significant losses to banks and insurance entities. They also demonstrated the importance of using accurate equity risk models and having a risk management function able to implement effective hedging strategies. Stock volatility forecasts play a key role in the estimation of equity risk and, thus, in the management actions carried out by financial institutions. Therefore, this paper has the aim of proposing more accurate stock volatility models based on novel machine and deep learning techniques. This paper introduces a neural network-based architecture, called Multi-Transformer. Multi-Transformer is a variant of Transformer models, which have already been successfully applied in the field of natural language processing. Indeed, this paper also adapts traditional Transformer layers in order to be used in volatility forecasting models. The empirical results obtained in this paper suggest that the hybrid models based on Multi-Transformer and Transformer layers are more accurate and, hence, they lead to more appropriate risk measures than other autoregressive algorithms or hybrid models based on feed forward layers or long short term memory cells.

Population statistics show that there was an increase in life expectancy during the last century. However, this fact hides that this increase was not equal for all groups of the population. One of the most problematic cases for measuring this increase is that of the dependent population because of the absence of specific statistics. This paper describes a methodology for calculating life expectancy using multistate models that take into account the diversity of situations considered by Spanish legislation. For this purpose, statistical information contained in the national survey on disability and dependency (EDAD 2008) is used. The results suggest that life expectancies are lower than those of the general population and that they differ according to gender and intensity of suffering from this contingency. The calculations were made considering the legal framework currently existing in Spain. This fact conditions the definition of dependent person and, therefore, the set of individuals, their characteristics, and therefore, their final results.

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