## 2014 |

Coppola, Mariarosaria; D’Amato, Valeria Basis risk in Solvency Capital Requirements for longevity risk (Journal Article) Investment Management and Financial Innovations, 11 (3), pp. 53-57, 2014. (Abstract | Links | BibTeX | Tags: Basis risk, Longevity Risk, net asset value, Solvency Capital Requirement) @article{Coppola2014a, title = {Basis risk in Solvency Capital Requirements for longevity risk}, author = {Mariarosaria Coppola and Valeria D’Amato}, url = {http://www.labstat.it/home/wp-content/uploads/2016/04/imfi_en_2014_03_Coppola.pdf}, year = {2014}, date = {2014-01-01}, journal = {Investment Management and Financial Innovations}, volume = {11}, number = {3}, pages = {53-57}, abstract = {The international guidelines of Solvency II prescribe a regulation which should help insurance industry mitigating undesired outcomes arising from the exposure to the systemic risks. In particular, the rules on Solvency Capital Requirements recommend to separately compute them for each risk factor, where for the longevity risk sub-module the Solvency Capital Requirement results by the change in net asset value (NAV) due to a longevity shock which actually assumes a permanent reduction of the mortality rates for all ages by 20%. Nevertheless, the data based on statistics coming from various national longevity indices differ from those deriving from the regulatory assessment of solvency, determining significant underestimations or overestimations: a basis risk comes from a questionable adequacy of the longevity shock. This paper contributes to the discussion on Solvency Capital Requirements by focusing on the main features of the potential basis risk which determines the inappropriate capitalization of insurance companies. Furthermore we analyze the sensitivities of the basis risk to different ages for better assessing the actual risk of insurance portfolios. }, keywords = {Basis risk, Longevity Risk, net asset value, Solvency Capital Requirement}, pubstate = {published}, tppubtype = {article} } The international guidelines of Solvency II prescribe a regulation which should help insurance industry mitigating undesired outcomes arising from the exposure to the systemic risks. In particular, the rules on Solvency Capital Requirements recommend to separately compute them for each risk factor, where for the longevity risk sub-module the Solvency Capital Requirement results by the change in net asset value (NAV) due to a longevity shock which actually assumes a permanent reduction of the mortality rates for all ages by 20%. Nevertheless, the data based on statistics coming from various national longevity indices differ from those deriving from the regulatory assessment of solvency, determining significant underestimations or overestimations: a basis risk comes from a questionable adequacy of the longevity shock. This paper contributes to the discussion on Solvency Capital Requirements by focusing on the main features of the potential basis risk which determines the inappropriate capitalization of insurance companies. Furthermore we analyze the sensitivities of the basis risk to different ages for better assessing the actual risk of insurance portfolios. |

## 2013 |

Coppola, Mariarosaria; D’Amato, Valeria; Levantesi, Susanna; Menzietti, Massimiliano; Russolillo, Maria Longevity risk hedging and basis risk (Proceeding) 2013. (Abstract | BibTeX | Tags: Basis risk, FDM, functional demographic model, Longevity Risk) @proceedings{Coppola2013, title = {Longevity risk hedging and basis risk}, author = {Mariarosaria Coppola and Valeria D’Amato and Susanna Levantesi and Massimiliano Menzietti and Maria Russolillo}, year = {2013}, date = {2013-07-03}, booktitle = {The 17th International Congress on Insurance: Mathematics and Economics, Copenhagen, July 1-3, 2013}, pages = {40-41}, abstract = {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 ("hedging population") and the population of members of a pension plan or the beneficiaries of an annuity portfolio ("exposed population") determines a signicant heterogeneity which causes the so-called basis risk. The paper focuses on the longevity risk management by securitization, providing a framework for measuring the basis risk impact on the hedging strategies. To this aim we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting.In order to quantify the basis risk, we define a stochastic mortality model for two populations based on the FDM framework. We consider both an independent FDM (the hedging population is independent from the exposed population) and a joint FDM (both populations are jointly driven by a single index of mortality over time). Under the proposed mortality model, we build a longevity hedging strategy involving a portfolio of q-forwards calibrated through the key-q-duration (KQD), i.e. the annuity portfolios price sensitivity to a shift in a key mortality rate . The shifts are adjusted with the standard deviation of the exposed population mortality in order to realise a more effective hedge. In order to analyse the hedge effectiveness we consider the present value of both unexpected cash flows of the insurance portfolio and payoffs from the q-forwards involved in the hedging portfolio. The KQD of these quantities as well as an adjustment factor depending on the specified mortality model allow to find the required notional amount of the q-forwards in presence of basis risk.}, keywords = {Basis risk, FDM, functional demographic model, Longevity Risk}, pubstate = {published}, tppubtype = {proceedings} } 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 ("hedging population") and the population of members of a pension plan or the beneficiaries of an annuity portfolio ("exposed population") determines a signicant heterogeneity which causes the so-called basis risk. The paper focuses on the longevity risk management by securitization, providing a framework for measuring the basis risk impact on the hedging strategies. To this aim we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting.In order to quantify the basis risk, we define a stochastic mortality model for two populations based on the FDM framework. We consider both an independent FDM (the hedging population is independent from the exposed population) and a joint FDM (both populations are jointly driven by a single index of mortality over time). Under the proposed mortality model, we build a longevity hedging strategy involving a portfolio of q-forwards calibrated through the key-q-duration (KQD), i.e. the annuity portfolios price sensitivity to a shift in a key mortality rate . The shifts are adjusted with the standard deviation of the exposed population mortality in order to realise a more effective hedge. In order to analyse the hedge effectiveness we consider the present value of both unexpected cash flows of the insurance portfolio and payoffs from the q-forwards involved in the hedging portfolio. The KQD of these quantities as well as an adjustment factor depending on the specified mortality model allow to find the required notional amount of the q-forwards in presence of basis risk. |

## 2012 |

Coppola, Mariarosaria; D’Amato, Valeria; Levantesi, Susanna; Menzietti, Massimiliano; Russolillo, Maria Managing basis risk in longevity hedging strategies (Proceeding) 2012. (Abstract | BibTeX | Tags: Basis risk, FDM, Longevity Risk) @proceedings{Coppola2012b, title = {Managing basis risk in longevity hedging strategies}, author = {Mariarosaria Coppola and Valeria D’Amato and Susanna Levantesi and Massimiliano Menzietti and Maria Russolillo}, year = {2012}, date = {2012-09-07}, booktitle = {1st European Actuarial Journal Conference. University of Lausanne and Swiss Association of Actuaries, 6-7 September 2012}, pages = {79-80}, abstract = {In the last years significant tools have been developed for transferring longevity risk to the capital markets, bringing additional capacity, flexibility and transparency to complement existing insurance solutions. Specifically, hedging longevity risk with index-based longevity hedges can have several advantages but the difference between the insurer’s mortality experience based on annuitant mortality and the hedged standardized index based on reference population mortality gives rise to the so-called basis risk. The presence of basis risk means that hedge effectiveness will not be perfect and that, post implementation, the hedged position will still have some residual risk. The present paper seeks to contribute to that literature by setting out a framework for quantifying the basis risk. In particular we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting. The literature suggests that the FDM forecast accuracy is arguably connected to the model structure, combining functional data analysis, nonparametric smoothing and robust statistics. In particular, the decomposition of the fitted curve via basis functions represents the advantage, since they capture the variability of the mortality trend, by separating out the effects of several orthogonal components. Specifically, while most existing models are designed for a single population the research objective is to model mortality of two populations as in Li and Hardy (2011) in order to align with the hedging purpose. Under the proposed mortality model, we develop an optimal longevity hedging strategy involving mortality linked securities and following the immunization theory approach. We firstly assume no difference between the two population mortalities (no basis risk) and we show as such a strategy could be not perfectly effective when difference in the reference population respect to mortality index’ one emerges and basis risk is measured. Afterwards an optimal hedging strategies is developed explicitly including basis risk. We show as the longevity hedging could be more effective although still not perfect.}, keywords = {Basis risk, FDM, Longevity Risk}, pubstate = {published}, tppubtype = {proceedings} } In the last years significant tools have been developed for transferring longevity risk to the capital markets, bringing additional capacity, flexibility and transparency to complement existing insurance solutions. Specifically, hedging longevity risk with index-based longevity hedges can have several advantages but the difference between the insurer’s mortality experience based on annuitant mortality and the hedged standardized index based on reference population mortality gives rise to the so-called basis risk. The presence of basis risk means that hedge effectiveness will not be perfect and that, post implementation, the hedged position will still have some residual risk. The present paper seeks to contribute to that literature by setting out a framework for quantifying the basis risk. In particular we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting. The literature suggests that the FDM forecast accuracy is arguably connected to the model structure, combining functional data analysis, nonparametric smoothing and robust statistics. In particular, the decomposition of the fitted curve via basis functions represents the advantage, since they capture the variability of the mortality trend, by separating out the effects of several orthogonal components. Specifically, while most existing models are designed for a single population the research objective is to model mortality of two populations as in Li and Hardy (2011) in order to align with the hedging purpose. Under the proposed mortality model, we develop an optimal longevity hedging strategy involving mortality linked securities and following the immunization theory approach. We firstly assume no difference between the two population mortalities (no basis risk) and we show as such a strategy could be not perfectly effective when difference in the reference population respect to mortality index’ one emerges and basis risk is measured. Afterwards an optimal hedging strategies is developed explicitly including basis risk. We show as the longevity hedging could be more effective although still not perfect. |

Coppola, Mariarosaria; D’Amato, Valeria; Levantesi, Susanna; Menzietti, Massimiliano; Russolillo, Maria Measuring and Hedging the basis risk by Functional Demographic Models (Journal Article) Mathematical Methods in Economics and Finance, 7 (1), pp. 19-39, 2012, ISSN: 1971-6419. (Abstract | Links | BibTeX | Tags: Basis risk, FDM, Lee Carter model, q-forward) @article{Coppola2012, title = {Measuring and Hedging the basis risk by Functional Demographic Models}, author = {Mariarosaria Coppola and Valeria D’Amato and Susanna Levantesi and Massimiliano Menzietti and Maria Russolillo}, url = {http://www.labstat.it/home/wp-content/uploads/2016/04/06-Coppola_DAmato_Levantesi_Menzietti_Russolillo-m2ef2012-7.pdf}, issn = {1971-6419}, year = {2012}, date = {2012-01-01}, journal = {Mathematical Methods in Economics and Finance}, volume = {7}, number = {1}, pages = {19-39}, publisher = {Department of Economics of the University Ca’ Foscari of Venice, Italy}, abstract = {Longevity phenomenon is a relevant aspect for insurance companies which are obliged to quantify the impact of uncertainty of mortality trend on issued products, in order to manage the risk derived from it. Recently, significant tools have been developed for transferring longevity risk to the capital markets, bringing additional capacity, flexibility and transparency to complement existing insurance solutions. In particular, hedging longevity risk with index-based longevity hedges can have several advantages. Nevertheless, the difference between the insurer’s mortality experience based on annuitant mortality and the hedged standardized index based on reference population mortality give rise to the so-called basis risk. The presence of basis risk means that hedge effectiveness will not be perfect and that, post implementation, the hedged position will still have some residual risk. The present paper seeks to contribute to that literature by setting out a framework for quantifying the basis risk. In particular we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model setting. Moreover, while most existing models are designed for a single population the research objective is to model mortality of two populations, in order to align with the hedging purpose. Finally, longevity hedging strategies are developed by involving mortality-linked securities.}, keywords = {Basis risk, FDM, Lee Carter model, q-forward}, pubstate = {published}, tppubtype = {article} } Longevity phenomenon is a relevant aspect for insurance companies which are obliged to quantify the impact of uncertainty of mortality trend on issued products, in order to manage the risk derived from it. Recently, significant tools have been developed for transferring longevity risk to the capital markets, bringing additional capacity, flexibility and transparency to complement existing insurance solutions. In particular, hedging longevity risk with index-based longevity hedges can have several advantages. Nevertheless, the difference between the insurer’s mortality experience based on annuitant mortality and the hedged standardized index based on reference population mortality give rise to the so-called basis risk. The presence of basis risk means that hedge effectiveness will not be perfect and that, post implementation, the hedged position will still have some residual risk. The present paper seeks to contribute to that literature by setting out a framework for quantifying the basis risk. In particular we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model setting. Moreover, while most existing models are designed for a single population the research objective is to model mortality of two populations, in order to align with the hedging purpose. Finally, longevity hedging strategies are developed by involving mortality-linked securities. |

# Publications

AR metric ARFIMA models ARIMA models ARMA models autoregressive metric Basis risk cluster analysis consumer perceptions consumer preferences Correspondence analysis covariates CUB model CUB models economic analysis food preferences food quality Hydrological time series Longevity Risk Mixture model multiple correspondence analysis multivariate analysis ordinal data series data Solvency Capital Requirement Solvency II statistical analysis statistical methods statistical model time series analysis time series classification

## 2014 |

Basis risk in Solvency Capital Requirements for longevity risk (Journal Article) Investment Management and Financial Innovations, 11 (3), pp. 53-57, 2014. |

## 2013 |

Longevity risk hedging and basis risk (Proceeding) 2013. |

## 2012 |

Managing basis risk in longevity hedging strategies (Proceeding) 2012. |

Measuring and Hedging the basis risk by Functional Demographic Models (Journal Article) Mathematical Methods in Economics and Finance, 7 (1), pp. 19-39, 2012, ISSN: 1971-6419. |