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.
Managing basis risk in longevity hedging strategies / Coppola, Mariarosaria; D’Amato, V.; Levantesi, S.; Menzietti, M.; Russolillo, M.. - (2012). (Intervento presentato al convegno 1st European Actuarial Journal Conference. University of Lausanne and Swiss Association of Actuaries tenutosi a Lausanne nel 6-7 September 2012).
Managing basis risk in longevity hedging strategies
COPPOLA, MARIAROSARIA;
2012
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
