Asymmetry in mortality volatility and its implications on index-based longevity hedging

Mortality volatility is crucially important to many aspects of index-based longevity hedging, including instrument pricing, hedge calibration and hedge performance evaluation. This paper sets out to develop a deeper understanding of mortality volatility and its implications on index-based longevity hedging. First, we study the potential asymmetry in mortality volatility by considering a wide range of generalised autoregressive conditional heteroskedasticity (GARCH)-type models that permit the volatility of mortality improvement to respond differently to positive and negative mortality shocks. We then investigate how the asymmetry of mortality volatility may impact index-based longevity hedging solutions by developing an extended longevity Greeks framework, which encompasses longevity Greeks for a wider range of GARCH-type models, an improved version of longevity vega, and a new longevity Greek known as “dynamic Delta”. Our theoretical work is complemented by two real-data illustrations, the results of which suggest that the effectiveness of an index-based longevity hedge could be significantly impaired if the asymmetry in mortality volatility is not taken into account when the hedge is calibrated.

Hedging Price Risk in the Presence of Quantity Risk

This research looks into hedge strategies to resolve foreign exchange-related risks, generated when investing in overseas financial assets, as an example of quantity risk. If an investor has information with no uncertainty over the volume and there is only a price risk he want to hedge, an investor will be able to reduce or eliminate risks by using relative derivative securities such as forwards or futures contracts. However, if there are uncertainties over the volume of hedging targets that is called quantity risk, it is impossible to set the optimal hedge ratio with the traditional method without considering the presence of quantity risk. In this paper, we theoretically draw an optimal hedge ratio which is estimated via minimal variance criterion under static hedge structure. We also analyze its hedge performance and the impact of change in covariance on the optimal hedge ratio and variance of investment return denominated as its own country currency. For theoretical approach, we review the impact that overseas financial assets’ yield and exchanges rates distribution will have on optimal hedge ratio through simple numerical analysis. Empirical analysis is carried out by using the stock indices of the U.S., Europe and Asian countries, and the results indicate that hedge strategies taken with quantity risk for all markets produced better hedging performance than the strategies taken without quantity risk. Since there is a need for systematic research on risks involving foreign exchanges that occur in the event of foreign investments aimed to develop the domestic financial industry, we hope that our research serve as a stepping-stone for further research.