Measuring and hedging the basis risk by Functional Demographic Models

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, flex- ibility 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 in- surer’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 ef- fectiveness will not be perfect and that, post implementation, the hedged position will still have some residual risk. The present paper seeks to con- tribute 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 pop- ulations, in order to align with the hedging purpose. Finally, longevity hedging strategies are developed by involving mortality-linked securities.