附保證終身提領(GLWB)變額年金為歐美市場廣受歡迎的退休商品設計，其提供變額年金在清償期終身分期領的功能，不論帳戶表現如何，在活的時候皆確定可領取約定的保證金額，對於民眾在因應退休生活有一定的吸引力。本研究主要探討終身提領商品之風險評估及避險策略，由於提供保證提領的保險公司會面對權益市場之不確定以及壽命改善現象所造成之風險，該風險為系統性之風險，國際監理機關要求保險公司必需採用隨機模型反應金融市場及環境的變化來評估準備金及風險資本如Solvency II。本研究提出創新的研究想法，透過避險策略如商品設計來降低長壽風險，以及投資組合波動度的方式來降低權益風險，並分析其在監理資本要求下之效益，研究分三年期解決三個議題。第一年主要探討GLWB商品的長壽風險的避險策略，除分析該商品若結合附保證最低死亡給付設計或納入人壽保險之最適內部避險外，亦考量外部避險效益，即透過長壽衍生性金融商品來避險，研究亦納入死亡率及權益隨機模型的架構，為降低基差風險，研究是採用Lee Carter架構下之VECM死亡率預測模型，由於GLWB亦涉略權益風險，本研究延伸Wang et al. (2017)所提出之regime-switching generalized hyperbolic 模型，透過最小變異方法求得長壽風險對於保險公司獲利影響最低之最適避險策略，並檢視計算不同避險策略的有效性。研究另個策略是建構一低波動投資組合以降低GLWB商品發行之風險資本並能兼顧保戶投資帳戶之效益，因此，第二年的研究主題是建構多資產指數組合之權益模型，並擬以Copulas方法來補捉多資產指數間之相關性，並在多資產指數組合架構下來評估風險資本。在權益模型的部份，將比較在不同權益模型下Copulas方法的配適度，包括延伸Wang et al. (2017) 單一資產模型為多資產的型式。在Copulas的部份，將考量對稱及不對稱之型式，並採用Kojadinovic and Yan (2010) and R'emillard (2017) 所提出之copula test 來檢視配適度。研究第三年則提出在風險資本要求下之最適低波動投資組合配置，並同時考量第一年的長壽風險及多資產指數建構下之避險效益, 研究將納入Solvency II下清償資本之計算，研究所提出之方法及架構可做為監理機關及保險公司在GLWB商品開發的參考。 ;According the VAs markets in the U.S. and in Europe, guaranteed lifetime withdrawal benefit (GLWB) products have become more and more popular in funding the retirement income. The design of VAs with GLWB gives the policyholders to accumulate assets during an accumulation phase but also provide the guaranteed income during a deccumulation phase no matter how the investments perform. Issuing GLWB involves not only the equity risk but also the longevity risk. Such risk is systematic and not diversifiable. The regulator has required the insurer to assess the guaranteed risk using the stochastic model that can take into account the current financial market condition. In this research, we consider the hedging strategy and utilize the product design to reduce the longevity risk and equity risk and the corresponding capital requirement. In the first-year project, we examine the internal longevity hedging strategy and the external longevity hedging strategy, respectively. The former strategy attempts to reduce the risk by offsetting product lines or utilizing product designs and the later strategy considers the use of the longevity derivatives. The optimal hedging strategy is obtained by a minimizing-variance approach that can minimize the impact of longevity risk on the insurer’s profit function. We also consider the basis risk in our hedging strategy. Thus, we employ the well-known Lee-Carter framework with the VECM mortality forecasting structure. The equity dynamic follows Wang et al. (2017)’s regime-switching generalized hyperbolic model. The hedge effectiveness of different approached are investigated numerically. To deal with the equity risk, this research proposes an investment strategy to explore a managed risk fund to mitigate drawdown risk and decreases hedge cost. Therefore, in the second-year project, we attempt to build a multi-equity index model using copula approach which can capture the dependence structure among the equity indices. We consider a variety of equity model including Wang et al. (2017)’s regime-switching generalized hyperbolic model. The goodness of fits of the copula functions are examined using the copula test by Kojadinovic and Yan (2010) and R'emillard (2017). In the third-year project, we find the optimal investment strategy by minimizing the solvency risk requirement. The solvency II capital requirement will be investigated. We also re-evaluate the hedging strategy investigated in the first year incorporating the investment strategy.
