The recent SARS-CoV-2 pandemic has involved several aspects of society, from healthcare to economics. In this framework, after staying on the edge at first, now the insurers are starting to play a fundamental role. The present research project aims to study the management of the risk sources associated with pandemics, providing adequate hedging techniques. To do this, we will transfer the aforementioned risks to the capital market, in order to face the problem from a financial perspective. In particular, we will highlight the role of pandemic events in the assessment of appropriate insurance products ascribed to the so called PRIIPs, whose value depends on suitable dynamics related to mortality. Moreover, we will describe the best models to represent the occurrence of shocks in mortality, we will furnish analytical solutions and innovative numerical procedures to evaluate the price of the financial product involved, and we will provide suitable indicators to measure the goodness of the scenario performances.
The research project encompasses innovative proposals w.r.t. the current literature.
The first one concerns the inspection of a collection of stochastic models, able to fit the pandemic mortality case. More precisely, we will examine a general class of affine stochastic processes incorporating a jump component in order to catch peaks in the mortality dynamics, due to extreme mortality occurrences. To this purpose, we will investigate the construction of a proper threshold estimator to identify mortality intensity jumps and distinguish them from pure volatile realizations (e.g. volatility in elderly mortality). Moreover, we intend to achieve this goal by studying both the parametric estimator case and the non-parametric one, exploiting the suitability of machine and deep learning techniques, such as Artificial Neural Networks.
Comparing the current literature, we notice that some research works employ continuous jump-diffusion models to define the force of mortality, but not considering both the case of pandemic mortality and the threshold estimation problem. Therefore, a significant amount of empirical evidences stemming from catastrophe mortality events (e.g. the current SARS-CoV-2 pandemic) have not been considered in mortality intensity modeling yet. However, a uniform treatment of the mortality dynamics is necessary to provide an accurate measurement of the ILS and ILD underlying, in a real-world context, as well as to exploit the appropriateness of standard securities and derivatives pricing techniques in a risk-neutral framework.
The pricing of ILS and ILD is a second innovative point. Doubtless, the Life Market allows the investors to provide for financial assets that are not correlated with the traditional ones and, at same time, hedging opportunities on excess of risks related to the human lifetime. These financial advantages are offset by the market incompleteness, implying significative difficulties to get the ILS or ILD fair price following a no-arbitrage scheme. For this reason, the current literature shows alternative pricing techniques, also embedding the market price of risk assessment, and essentially based on the Wang transform approach. Technically speaking, the latter method cannot grant a closed-form formula describing the transformed probability distributions of underlying, so that numerical procedures are needed. Therefore, we would develop a risk-neutral framework to price the ILS and ILD in an arbitrage-free context. Since the Life Market is incomplete, there exists an infinite number of risk-neutral probability measures equivalent to the physical one. To solve this problem, we will study a mathematical criterion to select the unique risk-neutral probability measure compliant to the specific ILS or ILD considered in a no free-lunch sense. At same time, if ILS or ILD price formula is not available in a closed-form, we will probe the suitability of innovative numerical techniques, focusing in particular on bivariate trees that have not been applied in the actuarial literature yet.
Finally, looking at the VEV indicator, we would like to stress that the current literature only considers the standard measurement proposed by the PRIIPs Regulation. Therefore, in order to quantify the market risk measure and the credit risk measure through the VEV evaluation, a gaussian distribution distributions assumption for the market returns must be considered. However, given the occurrence of different viable models for the underlyings and the ILS or ILD considered, a more complex probabilistic characterization could emerge. Therefore, we aim at evaluating, for the first time in literature, how, and in what extent, an ad-hoc VEV quantification for the ILS and ILD in a pandemic mortality framework is walkable, remaining compliant with the PRIIPs Regulation provisions.