Search Results (8)

Population events such as natural disasters, pandemics, extreme weather, and wars might cause jumps that have an immediate impact on mortality rates. The recent COVID-19 pandemic has demonstrated that these events should not be treated as nonrepetitive exogenous interventions. Therefore, mortality models incorporating jump effects are particularly important to capture the adverse mortality shocks. The mortality models with jumps, which we consider in this study, differ in terms of the duration of the jumps–transitory or permanent–the frequency of the jumps, and the size of the jumps. To illustrate the effect of the jumps, we also consider benchmark mortality models without jump effects, such as the Lee-Carter model, Renshaw and Haberman model and Cairns-Blake-Dowd model. We discuss the performance of all the models by analysing their ability to capture the mortality deterioration caused by COVID-19. We use data from different countries to simulate the mortality rates for the pandemic and post-pandemic years and examine their accuracy in forecasting the mortality jumps due to the pandemic. Moreover, we also examine the jump-free and jump models in terms of their impact on insurance pricing, specifically term annuity and life insurance present values calibrated for both pre- and post-COVID data. Full article

The main purpose of coherent mortality models is to produce plausible, joint forecasts for related populations avoiding, e.g., crossing or diverging mortality trajectories; however, the coherence assumption is very restrictive and it enforces trends that may be at odds with data. In this paper we focus on coherent, two-sex mortality models and we prove, under suitable conditions, that the coherence assumption implies sex gap unimodality, i.e., we prove that the difference in life expectancy between women and men will first increase and then decrease. Moreover, we demonstrate that, in the model, the sex gap typically peaks when female life expectancy is between 30 to 50 years. This explains why coherent mortality models predict narrowing sex gaps for essentially all Western European countries and all jump-off years since the 1950s, despite the fact that the actual sex gap was widening until the 1980s. In light of these findings, we discuss the current role of coherence as the gold standard for multi-population mortality models. Full article

The genera Oryctolagus and Lepus (order Lagomorpha) are essential elements in the trophic chain in the Iberian Peninsula, being the main prey of many predators, including some highly endangered predators such as the Iberian lynx (Lynx pardinus). Myxomatosis, a disease producing tumorations in conjunctive tissues, and produced by the Myxoma Virus, has caused mass mortalities in rabbits (Oryctolagus cuniculus) for decades. Recently, the virus has jumped interspecifically from rabbits to hares, and this has created a depletion in hare populations, generating great concern. We analyzed the population dynamics and distribution of both lagomorph species in a Mediterranean agricultural area of the south of Spain since the 1990s with a combination of systematic and non-systematic data. The appearance of the outbreak in the Iberian hare (Lepus granatenis) in 2018 enabled us to undertake an opportunistic analysis of its effects on the spatial structure and assemblages, as well as on the niches of both species using PCA analyses and ordination techniques. Analysis of the mortality effect on daily and seasonal cycles was also conducted, and relations with the temporal dimension was tested using generalized lineal models (GLMs). In our results, in addition to population and temporal patterns, we could observe a restructuring in hare distribution after the mortality event, highlighting that prior to the outbreak, rabbit and hare populations were spatially differentiated, although with some overlaps and niche similarities. However, since the outbreak, hare populations have been excluded from rabbit areas, suggesting that in the absence of rabbits, the virus has more difficulties to infect hares. We also provide an overview of the effect of this population depletion on the ecological and socio-economic dimension of this region, pointing out the importance of this situation for the area. Full article

We present a mortality model where future stochastic changes in population-wide mortality are driven by a finite-state hierarchical Markov chain. A baseline mortality in an initial ‘Alive’ state is calculated as the average logarithm of the observed mortality rates. There are several more ‘Alive’ states and a jump to the next ‘Alive’ state leads to a change (typically, an improvement) in mortality. In order to estimate the model parameters, we minimized a weighted average quadratic distance between the observed mortality rates and expected mortality rates. A two-step estimation procedure was used, and a closed-form solution for the optimal estimates of model parameters was derived in the first step, which means that the model could be parameterized very fast and efficiently. The model was then extended to allow for age effects whereby stochastic mortality improvements also depend on age. Forecasting relies on state space augmentation and an innovations state space time series model. We show that, in terms of forecasting, our model outperforms a naïve model of static mortality within a few years. The Markov approach also permits an exact computation of mortality indices, such as the complete expectation of life and annuity present values, which are key in the life insurance and pension industries. Full article

Index-based hedging solutions are used to transfer the longevity risk to the capital markets. However, mismatches between the liability of the hedger and the hedging instrument cause longevity basis risk. Therefore, an appropriate two-population model to measure and assess longevity basis risk is required. In this paper, we aim to construct a two-population mortality model to provide an effective hedge against the basis risk. The reference population is modelled by using the Lee–Carter model with the renewal process and exponential jumps, and the dynamics of the book population are specified. The analysis based on the U.K. mortality data indicate that the proposed model for the reference population and the common age effect model for the book population provide a better fit compared to the other models considered in the paper. Different two-population models are used to investigate the impact of sampling risk on the index-based hedge, as well as to analyse the risk reduction regarding hedge effectiveness. The results show that the proposed model provides a significant risk reduction when mortality jumps and sampling risk are taken into account. Full article

Background and objectives: Childhood obesity is one of the main public health issues facing advanced societies. The Spanish population presents 28.6% overweight or obese adolescents, and Extremadura, 22.3%. Physical fitness is considered one of the most important health markers and a common predictor of morbidity and mortality caused by cardiovascular diseases. Thus, fitness tests are needed for health monitoring, especially in overweight and obese adolescents. Therefore, this study aimed to explore the relationship between body composition and physical fitness in adolescents and to analyse if there are differences in physical condition and body composition between the sexes, as well as to compare the different body mass index (BMI) categories to each other. This project also tried to find regression equations to predict the physical fitness test results. Materials and Methods: A total of 225 adolescents were recruited. Weight status was classified according to WHO 2007 standards. Body composition variables (i.e., BMI, fat mass (FM), FM percentage (FM%), and fat-free mass (FFM)) and physical fitness (standing long jump (SLJ), speed–agility (SA), cardiorespiratory fitness (CF), and handgrip strength (HS)) were assessed. Results: Significant differences were found between the sexes in body composition (FM%, FM, and FFM) and physical fitness (SLJ, SA, CF, and HS) (p < 0.001) in favour of males. Significant differences were also found in speed (p = 0.002), CF (p < 0.001), and SLJ (p = 0.004) in favour of normal-weight adolescents compared to overweight and obese adolescents. Contrarily, the outcomes revealed a significantly greater HS (p = 0.014) in favour of overweight and obese participants compared to normal-weight adolescents. Moreover, the results showed that CF and SLJ correlated inversely with BMI, FM%, and total FM. There was also a direct relationship between SA and FM percentage, as well as between HS and FFM. Finally, four fitness test predictive models are proposed based on body composition, age, sex, and BMI. Conclusions: Overweight and obese adolescents have lower levels of physical fitness than their normal-weight peers, regardless of their sex. Normal-ranged body composition values are related to a greater physical fitness in adolescents. Furthermore, this study presents several equations that can help to predict the performance of different fitness tests in adolescents. Full article

Mortality forecasting has always been a target of study by academics and practitioners. Since the introduction and rising significance of securitization of risk in mortality and longevity, more in-depth studies regarding mortality have been carried out to enable the fair pricing of such derivatives. In this article, a comparative analysis is performed on the mortality forecasting accuracy of four mortality models. The methodology employs the Age-Period-Cohort model, the Cairns-Blake-Dowd model, the classical Lee-Carter model and the Kou-Modified Lee-Carter model. The Kou-Modified Lee-Carter model combines the classical Lee-Carter with the Double Exponential Jump Diffusion model. This paper is the first study to employ the Kou model to forecast French mortality data. The dataset comprises death data of French males from age 0 to age 90, available for the years 1900–2015. The paper differentiates between two periods: the 1900–1960 period where extreme mortality events occurred for French males and the 1961–2015 period where no significant jump is observed. The Kou-modified Lee-Carter model turns out to give the best mortality forecasts based on the RMSE, MAE, MPE and MAPE metrics for the period 1900–1960 during which the two World Wars occurred. This confirms that the consideration of jumps and leptokurtic features conveys important information for mortality forecasting. Full article

In this paper, we review pricing of the variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework and review the existing numerical methods. We also discuss pricing under the complete/incomplete financial market models, stochastic mortality and optimal/sub-optimal policyholder behavior, and in the presence of taxes. For numerical valuation of these contracts in the case of simple risky asset process, we develop a direct integration method based on the Gauss-Hermite quadratures with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is easier to implement and faster when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a numerical benchmark for practitioners and researchers developing pricing of variable annuity guarantees to assess the accuracy of their numerical implementation. Full article