Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk

By Luciano, Elisa; Regis, Luca et al. | Journal of Risk and Insurance, September 2017 | Go to article overview

Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk


Luciano, Elisa, Regis, Luca, Vigna, Elena, Journal of Risk and Insurance


INTRODUCTION

Longevity risk, that is, the risk of unexpected changes in survivorship, is now perceived as an important threat to the safety of insurance companies and pension funds. Most actors in the financial market are long longevity risk. This has stimulated the transformation of contracts subject to longevity risk into an asset class, as originally suggested by Blake and Burrows (2001). The creation of q-forwards, s-forwards, longevity bonds, and swaps represents a step in this direction, but this asset class is still in its infancy. In the meanwhile, insurance companies can benefit from natural hedging, that is, from natural offsetting between the longevity risk exposures of death benefits and life contracts, such as annuities. The importance of exploiting this natural offsetting extends beyond theory. Cox and Lin (2007) find empirical evidence that insurers whose liability portfolios benefit from natural hedging have a competitive advantage and charge lower premiums. Despite being safe, sound, and comparatively cheap, natural hedging is not trivial in the presence of longevity risk because the latter is difficult to capture per se in a parsimonious and manageable way and even more difficult to couple with a satisfactory model of financial risk, such as interest rate risk. However, the interactions between longevity and financial risk cannot be avoided from the perspective of immunization in the form of liability management, as the value of the reserves is subject to interest-rate risk, and a fortiori, from the perspective of asset and liability management (ALM).

Natural hedging of longevity risk without financial risk is recently addressed by Cox and Lin (2007), Wang et al. (2010), and Gatzert and Wesker (2012, 2013). Cox and Lin (2007), motivated by the empirical evidence mentioned above, propose the use of mortality swaps between annuity providers and life insurance writers. Wang et al. (2010) propose an immunization strategy that matches the duration and convexity of life insurance and annuity benefits. They demonstrate that this strategy is effective in reducing longevity risk by calibrating it to U.S. mortality data. However, they consider only liabilities, while we consider both assets and liabilities as well as financial risk. Gatzert and Wesker (2012) use simulations to select portfolios of policies that immunize the insurer's solvency against changes in mortality. Gatzert and Wesker (2013) consider the interactions among systematic, unsystematic, basis risk, and adverse selection in determining the effectiveness of natural hedging.

Natural hedging with financial risk is studied by Stevens et al. (2011). They show that financial risk has a clear impact on the overall initial riskiness of the annuity--life insurance mix. The effect of natural hedging may be overestimated when financial risk is ignored, affecting hedging possibilities. In their case, financial risk occurs only from potential losses from assets, while in our case, it affects both the assets and the fair value of liabilities.

We extend the existing literature in four directions. First, we model longevity and financial risk at the same time, and we assess their impact on the fair value of the insurer's net liabilities or reserves. We aim at hedging changes in reserves, at the first- and second-order approximations (delta and gamma hedging, respectively). The risk factors to hedge against are the differences between the mortality and interest-rate intensities forecasted today and their actual realizations in the future. Second, to hedge liabilities, we let the insurer use new sales of insurance contracts, reinsurance, and bonds, so we extend previous research by using both assets and liabilities for immunization. Third, we exploit hedging within a single generation and across generations (or across genders) to capture the fact that some products may be not marketed. For instance, death benefits for older generations may not be marketed. …

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