臺灣博碩士論文加值系統

附保證投資型保單準備金之提存必須反應該商品所會面臨之風險，故評估方法及精算假設的合理性便顯得相當重要。其中對於保戶行為之精算假設，不單受到保單內含之財物選擇權及附保證價值所影響，其中包含保戶年齡、保單價值大小以及保單持有期間等，皆能反應保戶的解約行為(Knoller et al. (2012))。本研究便以監理的角度出發，以保證最低提領給付(guaranteed minimum withdrawal benefit ; GMWB)為例，依照美國保險監理官協會(National Association of Insurance Commissioners ; NAIC)頒布之精算準則Actuarial Guideline XLIII (AG43)之規範，納入不同投資收益模型以及保戶型為進行分析。投資收益模型部分考量對數常態模型(LN)以及狀態轉換對數常態模型(RSLN2)，其中因狀態轉換對數常態模型厚尾的性質，其所計算之準備金金額較對數常態模型(LN)來的高。保戶行為部分，以中年族群來說，理性保戶行為在小型保單所需提存的準備金最高；大型保單則為Knoller et al. (2012)的保戶解約模型最高。顯示保戶行為假設不同對準備金會造成相當的影響，壽險公司必須依照自身的經驗資料擬訂相對應的解約率模型，如實提存反映真實風險的準備金數額。

Policyholder behavior is important for the reserve of investment guarantee products to reflect the real risk that insurer will meet. Knoller et al. (2012) presented that policyholder behavior is not only affected by the “in-the-moneyness” of the embedded financial options but also affected by the other factors such as policyholder’s financial literacy, age, policy size and curtate duration. Based on the insurance regulation, we analyze the impact of policyholder behaviors on reserving of variable annuities with guaranteed minimum withdrawal benefit (GMWB). Under the Actuarial Guideline XLIII (AG43) adopted by National Association of Insurance Commissioners, we consider different market models and policyholder behavior in our research. The results show that Regime Switching Lognormal model (RSLN-2) which follows heavy tail presents a higher reserve requirement rather than Lognormal model (LN). For the middle-aged adults, the optimal behavior presents the highest reserve requirement under the small policies. The regression model of Knoller et al. (2012) presents the highest reserve requirement under the large policies. Our analyses indicate significant impact between different policyholder behavior assumptions, so the insurers should use their experience to draw up their own surrender model to calculate the true reserve they need.

摘要--------------------------------------------------- i
Abstract----------------------------------------------ii
第一章、緒論---------------------------------------------1
第二章、文獻回顧------------------------------------------2
第三章、附保證商品準備金提存及監理規範------------------------4
3-1保證最低提領給付---------------------------------------4
3-2第43號精算作業準則-------------------------------------5
3-2-1 CTE(70)------------------------------------------6
3-2-2標準情境金額----------------------------------------7
第四章、模型架構-----------------------------------------10
4-1投資收益模型-----------------------------------------10
4-1-1對數常態模型---------------------------------------10
4-1-2狀態轉換對數常態模型--------------------------------11
4-1-3參數校正------------------------------------------13
4-2保戶行為假設-----------------------------------------16
4-2-1最小平方蒙地卡羅法----------------------------------16
4-2-2 Knoller et al. (2012)保戶解約模型-----------------17
第五章、數值分析-----------------------------------------19
5-1最小平方蒙地卡羅法------------------------------------19
5-2 Knoller et al. (2012)保戶解約模型-------------------22
5-3準備金結果分析---------------------------------------24
第六章、結論--------------------------------------------32
參考文獻-----------------------------------------------34

1. Agnew, J.R. (2006): Do Behavioral Biases Vary across Individuals? Evidence from Individual Level 401(k) Data, Journal of Financial and Quantitative Analysis 41(4), 939–962.

2. Augustyniak, M. & Boudreault, M. (2012): An Out-of-Sample Analysis of Investment Guarantees for Equity-Linked products - Lessons from the financial crisis of the late-2000s, North American Actuarial Journal 16(2), 183-206

3. American Academy of Actuaries (2005): Recommended Approach for Setting Regulatory Risk-Based Capital Requirements for Variable Annuities and Similar Products.

4. Bauer, D., Kling, A. & Russ, J. (2008): A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities, ASTIN Bulletin 38(2), 621–651.

5. Behrman, J.R., Mitchell, O.S., Soo, C. & Bravo, D. (2010): Financial Literacy, Schooling, and Wealth Accumulation, NBER Working Paper 16452.

6. Chen, Z., Vetzal, K. & Forsyth, P.A. (2008): The Effect of Modelling Parameters on The Value of GMWB Guarantees, Insurance: Mathematics and Economics 43(1), 165-173.

7. Hardy, M. R. (2001): A Regime Switching Model of Long Term Stock Returns, North American Actuarial Journal 5(2), 41-53.

8. Hardy, M. R. (2003): Investment Guarantees Modeling and Risk Management for Equity-Linked Life Insurance, John Wiley＆Sons.

9. Kling, A., Ruez, F. & Russ, J. (2011): The Impact of Policyholder Behavior on Pricing, Hedging, and Hedge Efficiency of Variable Annuity Guarantees, Working Paper.
35

10. Knoller, C., Kraut, G. & Schoenmaekers, P. (2012): On The Propensity to Surrender a Variable Annuity Contract - An Empirical Analysis of Dynamic Policyholder Behaviour, Munich Risk and Insurance Center Working Paper 7.

11. Longstaff, F.A. & Schwartz, E.S. (2001), Valuing American Options by Simulation: A Simple Least-Squares Approach, The Review of Financial Studies 14(1), 113-147.

12. Milevsky, M.A. & Salisbury, T.S. (2006): Financial valuation of guaranteed minimum withdrawal benefits, Insurance: Mathematics and Economics 38(1), 21–38.

13. Moenig, T. & Bauer, D. (2011): Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities, Working Paper, Georgia State University.

14. National Association of Insurance Commissioners (2008): Actuarial Guideline XLIII CARVM for Variable Annuities.

15. 湯可名(2009)，附投資保證型保險商品評價探討，東吳大學財務工程與精算數學研究所碩士論文。

16. 黃克崴(2008)，隨機投資模型在精算上的應用，東吳大學財務工程與精算數學研究所碩士論文。

17. 林忠機、楊曉文(2011)，附保證給付投資型保險之定價與風險評估，財團法人保險發展事業中心。