- 學位論文
跳躍模型下附解約選擇權之投資型保險商品定價
Pricing Equity-Linked Life Insurance Contract with a Surrender Option Under a Jump-Diffusion Model
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摘要
在本篇論文中，我們關注了一種附最低保證利率的投資型保險商品，此商品給予投資人在到期日前解約的權利。投資型保險是人壽保險商品中重要的一環，隨著市場發展，此種保險結合投資的複合式商品受到廣大的歡迎，也因此在商品的定價上需要多方面的考慮。在我們的研究中，主要將注意力放在保險公司給予投資人解約的權力，此權力稱為解約選擇權，或稱退保選擇權 (Surrender option)。解約選擇權的本質是一種美式賣權，因其是給予投資人在任何時間點將商品賣回給保險公司的權力。 為了評價這類商品，我們遵循 Bernard 和 Lemieux (2008) 針對附解約選擇權投資型保險商品評價的方法，同樣將死亡率風險納入評價模型中，並使用 Longstaff 和 Schwartz (2001) 提出用以評價美式賣權之最小平方蒙地卡羅模擬法 (Least-squares Monte Carlo simulation, LSM) 來模擬解約選擇權的定價。此外，我們假設此商品之投資標的資產服從 Kou (2002) 提出之股價雙指數分配跳躍模型。在 Kelani 和 Quittard-Pinon (2013) 的研究中，得知當跳躍事件發生時，解約選擇權之價值也會提升，因此我們延伸這個結論，進而探討影響雙指數分配的兩個參數 eta_1 和 eta_2，也就是向上跳躍與向下跳躍的幅度 (size) 與解約選擇權的定價會有什麼樣的相關性。並可以藉由探討向下跳躍之幅度變動對保險商品價值的影響，試著分析當金融危機發生頻率越高，意即股價持續下跌時，解約選擇權所扮演之角色的重要性。
並列摘要
In this paper, we focus on a guaranteed equity-linked life insurance contract which gives policyholders a right to surrender before the maturity time. The equity-linked life insurance contract is an important type of policies of the life insurance companies. As a growth of market, such products combined with insurance and investment becoming more popular than before and we need to pay more attention when pricing these contracts. The right to surrender, which called the surrender option, is one of the most important part in our study and can be seen as an American option. To pricing such contracts, we follow Bernard and Lemieux (2008) who take the mortality risk into account and use least-squares Monte Carlo (LSM) simulation approach suggested by Longstaff and Schwartz (2001) for pricing the American-style surrender option. Besides, we extend their model to consider the underlying assets following a jump-diffusion process described by Kou (2002), which assume that the index fund is an exponential of a Levy process. Kélani and Quittard-Pinon (2013) mention that the contract value is significantly positively related to the jump frequency. We further investigate whether the size of jump downward affect the valuation of the contract and the timing of surrender. Numerical results show that the contract value (surrender value) is positively related to the size of jump downward. When financial events have become more frequent and more severe, this study helps better understand the valuation of this product and its surrender behaviors.
參考文獻
[1] Albizzati, M.O. and Geman, H. (1994). Interest-rate Risk Management and Valuation of the Surrender Option in Life-Insurance Policies. Journal of Risk and Insurance 61, 616-637.
[2] Bacinello, A.R. (1993). Pricing Equity-Linked Life Insurance with Endogenous Minimum Guarantees. Insurance: Mathematics and Economics 12, 245-257.
[3] Bacinello, A.R. (2001). Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed. ASTIN BULLETIN 31, 275-297.
[4] Bacinello, A.R. (2003). Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option. Journal of Risk and Insurance 70, 461-487.
[5] Bernard, C. and Lemieux, C. (2008). Fast Simulation of Equity-Linked Life Insurance Contracts with a Surrender Option. In Simulation Conference, WSC 2008. Winter 444-452. IEEE.