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題名 最低提領保證變額年金：定價及動態最佳化避險
Guaranteed minimum withdrawal benefit annuity: Valuation and dynamic optimal hedge作者 何庭昀
Ho, Ting-Yun貢獻者 謝明華
Hsieh, Ming-Hua
何庭昀
Ho, Ting-Yun關鍵詞 GMWB 定價
GMWB 動態避險
O-GARCH
GMWB valuation
GMWB dynamic hedging
O-GARCH日期 2019 上傳時間 5-九月-2019 15:48:07 (UTC+8) 摘要 本研究在不考慮死亡率的假設下，探討收取比例費用及固定費用的最低提領保證變額年金（Guaranteed Minimum Withdrawal Benefit, GMWB）之定價及動態避險之方法，並以例子來觀察動態避險在模擬資料中損益現值的分佈，及歷史資料的動態避險結果。GMWB 的定價，與每期保險公司所收之費用及被保險人提領的金額有關，不易推導定價公式。因此我們假設已知被保險人未來提領情境，並以風險中立評價模型、 GMWB 保險商品模型及蒙地卡羅模擬法，在 Q-measure 下進行定價。避險則以市場上可購買，且與投資標的相關性高的避險資產，進行動態避險策略的建構。本研究使用正交廣義自回歸條件異方差模型（Orthogonal Generalized Auto Regressive Conditional Heteroskedasticity, O-GARCH）來估計避險資產及 GMWB 價值的共同分佈，計算各個避險資產最佳化避險比例，最小化 GMWB 價值變化的變異數。在最後與傳統上常用的 Delta 避險與不避險的情境進行比較，觀察在 P-measure 情境下，保險公司在避險前後損益現值分佈的差別。
This paper investigates in valuation and hedging of Guaranteed Minimum Withdrawal Benefit (GMWB) variable annuity, and demonstrating the results of dynamic optimal hedging on simulated data and historical data.The value of GMWB is related to fees and withdrawals, and it is hard to be valued with formula. Therefore, given the withdrawal schedule, we can value GMWB with the risk-neutral valuation method and the Monte Carlo method in Q-measure.The goal of dynamic optimal hedging strategy is to minimize volatility of hedging errors. We choose hedging assets with high return correlation with the underlying asset and computing optimal hedging ratios of hedging assets with the joint probability distribution of assets to minimize the volatility of hedging errors. The joint probability distribution can be derived from the orthogonal generalized autoregressive conditional heteroskedasticity model (O-GARCH). At the end of this paper, we compare optimal hedging with delta hedging and un-hedging, concluding the hedging performance of optimal hedging.參考文獻 Alexander, C. (2000). A primer on the orthogonal GARCH model. manuscript ISMA Centre, University of Reading, UK, 2.Anderson, R. W., & Danthine, J.-P. (1981). Cross hedging. Journal of Political Economy, 89(6), 1182-1196.Baillie, R. T., & Myers, R. J. (1991). Bivariate GARCH estimation of the optimal commodity futures hedge. Journal of Applied Econometrics, 6(2), 109-124.Coleman, T. F., Li, Y., & Patron, M.-C. (2006). Hedging guarantees in variable annuities under both equity and interest rate risks. Insurance: Mathematics and Economics, 38(2), 215-228.Glasserman, P. (2003). Monte Carlo methods in financial engineering (Vol. 53).Hardy, M. (2003). Investment guarantees: Modeling and risk management for equity-linked life insurance.Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic theory, 20(3), 381-408.Harrison, J. M., & Pliska, S. R. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic processes and their applications, 11(3), 215-260.Hsieh, M. H., & Kuo, W. A. (2014). Generating economics scenarios for the long-term solvency assessment of life insurance companies : The orthogonal ARMA-GARCH method.Hsieh, M. H., Wang, J. L., Chiu, Y. F., & Chen, Y. C. (2018). Valuation of variable long-term care annuities with guaranteed lifetime withdrawal benefits: A variance reduction approach. Insurance: Mathematics and Economics, 78, 246-254. 描述 碩士
國立政治大學
風險管理與保險學系
106358010資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106358010 資料類型 thesis dc.contributor.advisor 謝明華 zh_TW dc.contributor.advisor Hsieh, Ming-Hua en_US dc.contributor.author (作者) 何庭昀 zh_TW dc.contributor.author (作者) Ho, Ting-Yun en_US dc.creator (作者) 何庭昀 zh_TW dc.creator (作者) Ho, Ting-Yun en_US dc.date (日期) 2019 en_US dc.date.accessioned 5-九月-2019 15:48:07 (UTC+8) - dc.date.available 5-九月-2019 15:48:07 (UTC+8) - dc.date.issued (上傳時間) 5-九月-2019 15:48:07 (UTC+8) - dc.identifier (其他 識別碼) G0106358010 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/125541 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 風險管理與保險學系 zh_TW dc.description (描述) 106358010 zh_TW dc.description.abstract (摘要) 本研究在不考慮死亡率的假設下，探討收取比例費用及固定費用的最低提領保證變額年金（Guaranteed Minimum Withdrawal Benefit, GMWB）之定價及動態避險之方法，並以例子來觀察動態避險在模擬資料中損益現值的分佈，及歷史資料的動態避險結果。GMWB 的定價，與每期保險公司所收之費用及被保險人提領的金額有關，不易推導定價公式。因此我們假設已知被保險人未來提領情境，並以風險中立評價模型、 GMWB 保險商品模型及蒙地卡羅模擬法，在 Q-measure 下進行定價。避險則以市場上可購買，且與投資標的相關性高的避險資產，進行動態避險策略的建構。本研究使用正交廣義自回歸條件異方差模型（Orthogonal Generalized Auto Regressive Conditional Heteroskedasticity, O-GARCH）來估計避險資產及 GMWB 價值的共同分佈，計算各個避險資產最佳化避險比例，最小化 GMWB 價值變化的變異數。在最後與傳統上常用的 Delta 避險與不避險的情境進行比較，觀察在 P-measure 情境下，保險公司在避險前後損益現值分佈的差別。 zh_TW dc.description.abstract (摘要) This paper investigates in valuation and hedging of Guaranteed Minimum Withdrawal Benefit (GMWB) variable annuity, and demonstrating the results of dynamic optimal hedging on simulated data and historical data.The value of GMWB is related to fees and withdrawals, and it is hard to be valued with formula. Therefore, given the withdrawal schedule, we can value GMWB with the risk-neutral valuation method and the Monte Carlo method in Q-measure.The goal of dynamic optimal hedging strategy is to minimize volatility of hedging errors. We choose hedging assets with high return correlation with the underlying asset and computing optimal hedging ratios of hedging assets with the joint probability distribution of assets to minimize the volatility of hedging errors. The joint probability distribution can be derived from the orthogonal generalized autoregressive conditional heteroskedasticity model (O-GARCH). At the end of this paper, we compare optimal hedging with delta hedging and un-hedging, concluding the hedging performance of optimal hedging. en_US dc.description.tableofcontents 第一章 緒論 1第一節 研究動機與研究目的 1第二章 文獻回顧 3第三章 GMWB 定價模型 6第四章 最佳化避險策略 10第一節 O-GARCH 模型 10第二節 最佳化避險 13第三節 對照組 Delta 避險 15第五章 數值結果 17第一節 歷史回測 19第二節 未來模擬 21第六章 結論 24參考資料 25 zh_TW dc.format.extent 706595 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106358010 en_US dc.subject (關鍵詞) GMWB 定價 zh_TW dc.subject (關鍵詞) GMWB 動態避險 zh_TW dc.subject (關鍵詞) O-GARCH zh_TW dc.subject (關鍵詞) GMWB valuation en_US dc.subject (關鍵詞) GMWB dynamic hedging en_US dc.subject (關鍵詞) O-GARCH en_US dc.title (題名) 最低提領保證變額年金：定價及動態最佳化避險 zh_TW dc.title (題名) Guaranteed minimum withdrawal benefit annuity: Valuation and dynamic optimal hedge en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Alexander, C. (2000). A primer on the orthogonal GARCH model. manuscript ISMA Centre, University of Reading, UK, 2.Anderson, R. W., & Danthine, J.-P. (1981). Cross hedging. Journal of Political Economy, 89(6), 1182-1196.Baillie, R. T., & Myers, R. J. (1991). Bivariate GARCH estimation of the optimal commodity futures hedge. Journal of Applied Econometrics, 6(2), 109-124.Coleman, T. F., Li, Y., & Patron, M.-C. (2006). Hedging guarantees in variable annuities under both equity and interest rate risks. Insurance: Mathematics and Economics, 38(2), 215-228.Glasserman, P. (2003). Monte Carlo methods in financial engineering (Vol. 53).Hardy, M. (2003). Investment guarantees: Modeling and risk management for equity-linked life insurance.Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic theory, 20(3), 381-408.Harrison, J. M., & Pliska, S. R. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic processes and their applications, 11(3), 215-260.Hsieh, M. H., & Kuo, W. A. (2014). Generating economics scenarios for the long-term solvency assessment of life insurance companies : The orthogonal ARMA-GARCH method.Hsieh, M. H., Wang, J. L., Chiu, Y. F., & Chen, Y. C. (2018). Valuation of variable long-term care annuities with guaranteed lifetime withdrawal benefits: A variance reduction approach. Insurance: Mathematics and Economics, 78, 246-254. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU201900707 en_US
