scholarly journals Forward Mortality Rates in Discrete Time II: Longevity Risk and Hedging Strategies

2016 ◽  
Author(s):  
Andrew Hunt ◽  
David P. Blake
Keyword(s):  
Discrete Time ◽  
Mortality Rates ◽  
Longevity Risk ◽  
Hedging Strategies

A longevity basis risk analysis in a joint FDM framework

2017 ◽  
Vol 18 (1) ◽  
pp. 55-75
Author(s):  
Valeria D’Amato ◽  
Mariarosaria Coppola ◽  
Susanna Levantesi ◽  
Massimiliano Menzietti ◽  
Maria Russolillo
Keyword(s):  
Functional Data ◽  
Mortality Rates ◽  
Longevity Risk ◽  
Demographic Model ◽  
Model Framework ◽  
Hedging Strategy ◽  
Basis Risk ◽  
Content Type ◽  
Mortality Curve ◽  
Hedging Strategies

Purpose The improvements of longevity are intensifying the need for capital markets to be used to manage and transfer the risk through longevity-linked securities. Nevertheless, the difference between the reference population of the hedging instrument and the population of members of a pension plan, or the beneficiaries of an annuity portfolio, determines a significant heterogeneity causing the so-called basis risk. In particular, it is shown that if insurers use financial instruments based on national indices to hedge longevity risk, this hedge can become imperfect. For this reason, it is fundamental to arrange a model allowing to quantify the basis risk for minimising it through a correct calibration of the hedging instrument. Design/methodology/approach The paper provides a framework for measuring the basis risk impact on the. To this aim, we propose a model that measures the population basis risk involved in a longevity hedge, in the functional data model setting. hedging strategies. Findings The innovative contribution of the paper occurs in two key points: the modelling of mortality and the hedging strategy. Regarding the first point, the paper proposes a functional demographic model framework (FDMF) for capturing the basis risk. The FDMF model generally designed for single population combines functional data analysis, nonparametric smoothing and robust statistics. It allows to capture the variability of the mortality trend, by separating out the effects of several orthogonal components. The novelty is to set the FDMF for modelling the mortality of the two populations, the hedging and the exposed one. Regarding the second point, the basic idea is to calibrate the hedging strategy determining a suitable mixture of q-forwards linked to mortality rates to maximise the degree of longevity risk reduction. This calibration is based on the key q-duration intended as a measure allowing to estimate the price sensitivity of the annuity portfolio to the changes in the underlying mortality curve. Originality/value The novelty lies in linking the shift in the mortality curve to the standard deviation of the historical mortality rates of the exposed population. This choice has been determined by the observation that the shock in a mortality rate is age dependent. The main advantage of the presented framework is its strong versatility, being the functional demographic setting a generalisation of the Lee-Carter model commonly used in mortality forecasting, it allows to adapt to different demographic scenarios. In the next developments, we set out to compare other common factor models to assess the most effective longevity hedge. Moreover, the parsimony for considering together two trajectories of the populations under consideration and the convergence of long-term forecast are important aspects of our approach.

scholarly journals Mortality data reliability in an internal model

2020 ◽  
Vol 14 (2) ◽  
pp. 420-444
Author(s):  
Fabrice Balland ◽  
Alexandre Boumezoued ◽  
Laurent Devineau ◽  
Marine Habart ◽  
Tom Popa
Keyword(s):  
Data Quality ◽  
Internal Model ◽  
Mortality Rates ◽  
Solvency Ii ◽  
West Germany ◽  
Mortality Data ◽  
Longevity Risk ◽  
Capital Requirement ◽  
Stochastic Mortality ◽  
The Impact

AbstractIn this paper, we discuss the impact of some mortality data anomalies on an internal model capturing longevity risk in the Solvency 2 framework. In particular, we are concerned with abnormal cohort effects such as those for generations 1919 and 1920, for which the period tables provided by the Human Mortality Database show particularly low and high mortality rates, respectively. To provide corrected tables for the three countries of interest here (France, Italy and West Germany), we use the approach developed by Boumezoued for countries for which the method applies (France and Italy) and provide an extension of the method for West Germany as monthly fertility histories are not sufficient to cover the generations of interest. These mortality tables are crucial inputs to stochastic mortality models forecasting future scenarios, from which the extreme 0.5% longevity improvement can be extracted, allowing for the calculation of the solvency capital requirement. More precisely, to assess the impact of such anomalies in the Solvency II framework, we use a simplified internal model based on three usual stochastic models to project mortality rates in the future combined with a closure table methodology for older ages. Correcting this bias obviously improves the data quality of the mortality inputs, which is of paramount importance today, and slightly decreases the capital requirement. Overall, the longevity risk assessment remains stable, as well as the selection of the stochastic mortality model. As a collateral gain of this data quality improvement, the more regular estimated parameters allow for new insights and a refined assessment regarding longevity risk.

scholarly journals Dynamic Hedging Strategies Based on Changing Pricing Parameters for Compound Ratchets

2019 ◽  
Vol 14 (1) ◽  
Author(s):  
Patrice Gaillardetz ◽  
Samia El Khoury
Keyword(s):  
Discrete Time ◽  
Equity Market ◽  
Dynamic Hedging ◽  
New Approach ◽  
Initial Capital ◽  
Market Growth ◽  
Hedging Strategies ◽  
The Right

Abstract Equity-Indexed Annuity products (EIAs) are becoming increasingly popular as they are accumulation vehicles that offer participation in the equity market growth while keeping the initial capital protected. This paper focuses in particular on a special type of EIAs; the Compound Ratchet (CR). Sellers of this product retain the right to change one of the pricing parameters on each contract anniversary date while promising not to cross a certain predetermined threshold. Changing these parameters can sometimes have an impact on the value of the EIA, which makes them interesting to study. In order to reproduce the pattern of these changing parameters, a new approach of dynamically hedging the CR EIA and simultaneously protecting the issuer from hedging risk is proposed and tested. Trading can only be done in discrete time, which produces hedging errors. Therefore, the new approach is applied to transfer these errors from the issuer to the buyer by dynamically changing the pricing parameters. The distribution of these parameters is extracted and analyzed.

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