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題名 考量死亡、利率、脫退與流動性風險下生死合險契約之盈餘分析
Surplus Analysis for Endowment Contracts Considering Mortality, Interest Rate, Surrender and Liquidity Risks
作者 林偉翔
Lin, Wei Hsiang
貢獻者 林士貴
Lin, Shih Kuei
林偉翔
Lin, Wei Hsiang
關鍵詞 脫退
隨機利率
生死合險
流動性風險
Surrender
Stochastic Interest Rate Process
Endowment Contract
Liquidity Risk
日期 2015
上傳時間 3-Aug-2015 13:21:40 (UTC+8)
摘要 當保險契約被發行時，保險公司必須被要求盡可能的具備承擔未來不可知的風險的能力。本文將死亡風險、利率風險、脫退風險以及流動性風險引入，並針對生死合險契約進行盈餘分析。在此以 Vasicek (1977) 所提出之隨機利率模型、根據被保險人理性行為作為基礎之脫退模型以及引入簡化後的 Longstaff、Mithal與Nies (2005)流動性風險債券價格來描述各種風險。根據上述模型假設下計算保費及準備金，遂以蒙地卡羅模擬法量化源於各種風險之盈餘。最後，本文計算保險公司之盈餘對各風險參數之敏感度分析，並計算各期破產與發生流動性問題之可能性。
Once insurance contracts are issued, the insurers should be capable to deal with the unknown conditions in the future as possible. In this paper, we analyze the impact of mortality, interest rate, surrender and liquidity risks on the surplus of endowment contract. We model the interest rate risk by Vasicek model, the surrender rate based on the rational behavior of policyholders and introduce the discounted price of zero coupon bonds as the liquidity risk. Under such assumptions, we compute the premium and reserve, demonstrate the simulated insurance surplus, and finally exhibit the statistics of the surplus from different sources. The simulated results show the sensitivity of the surplus to the parameters of the risks. At the same time, we also show the probabilities of insolvency and illiquidity of the insurer before the maturity date of the contract due to the fluctuating surrender rate and liquidity risk resulting from the stochastic interest rate.
參考文獻 [1] Albizzati, M. O., Geman, H., 1994. Interest rate risk management and valuation of the surrender option in life Insurance policies. The Journal of Risk and Insurance. Vol. 61, 616-637.
[2] Bauer, D., Kiesel, R., Kling, A., Ruβ, J., 2006. Risk neutral valuation of participating life insurance contracts. Insurance: Mathematics and Economics. Vol. 39, 171-183.
[3] Berkowitz, J., 2000b. Incorporating liquidity risk into value-at-risk models. The Journal of Derivatives. Working Paper, University of California, Irvine.
[4] Brigo, D., Mercurio, F., 2007. Interest rate models: Theory and practice with smile, inflation and credit. Springer-Verlag Berlin Heidelberg.
[5] Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J., 1997. Actuarial mathematics. In: The Society of Actuaries. Itasca, Illinois.
[6] De Giovanni, 2010. Lapse rate modeling: A rational expectation approach. Scandinavian Actuarial Journal. Vol. 1, 56-68.
[7] Eling, M., Kiesenbauer, D., 2013. What policy features determine life insurance lapse? An analysis of the German market. The Journal of Risk and Insurance. Vol. 81, 241-269.
[8] Eling, M., Kochanski, M., 2012. Research on lapse in life insurance: What has been done and what needs to be done? The Journal of Risk Finance. Vol. 14, 392 –413.
[9] Fier, S., Liebenberg, A.P., 2013. Life insurance lapse behavior. North American Actuarial Journal. Vol. 17, 153-167.
[10] Geneva Association, 2012. Surrenders in the Life Insurance Industry and Their Impact on Liquidity.
[11] Kuo, W., Tsai, C., Chen, W., 2003. An empirical study on the lapse rate: The cointegration approach. The Journal of Risk and Insurance. Vol. 70, 487-508.
[12] Le Courtois, O., Nakagawa, H., 2011. On surrender and default risks. Mathematical Finance, forthcoming.
[13] Loisel, S., Milhaud, X., 2011. From deterministic to stochastic surrender risk models: Impact of correlation crises on economics capital. European Journal of Operational Research. Vol. 214, 348-357.
[14] Longstaff, F.A., Mithal, S., Neis, E., 2005. Corporate yield spreads: Default risk of liquidity? Now evidence from credit default swap market. The Journal of Finance. Vol. LX, 2213-2253.
[15] Nolde, N., Parker, G., 2014. Stochastic analysis of insurance surplus. Insurance Mathematics and Economics. Vol. 56, 1-13.
[16] Smink, M., 1991. Risk measurement for asset liability matching a simulation approach to single premium deferred annuities, 2nd AFIR International Colloquium. Brighton 1991. Proceedings, Vo1. 2, 75-92.
[17] Tsai, C., Kuo, W., Chiang, D. M.-H., 2009. The distributions of policy reserves considering the policy-year structures of surrender rates and expense ratios. Journal of Risk and Insurance. Vol. 76, 909-931.
[18] Vasicek, O., 1977. An equilibrium characterization of the term structure. Journal of Financial Economics. Vol. 5, 177-188.
[19] Zenios, S. A., 1999. Financial optimization. Cambridge University Press.
描述 碩士
國立政治大學
金融研究所
102352001
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102352001
資料類型 thesis
dc.contributor.advisor 林士貴zh_TW
dc.contributor.advisor Lin, Shih Kueien_US
dc.contributor.author (Authors) 林偉翔zh_TW
dc.contributor.author (Authors) Lin, Wei Hsiangen_US
dc.creator (作者) 林偉翔zh_TW
dc.creator (作者) Lin, Wei Hsiangen_US
dc.date (日期) 2015en_US
dc.date.accessioned 3-Aug-2015 13:21:40 (UTC+8)-
dc.date.available 3-Aug-2015 13:21:40 (UTC+8)-
dc.date.issued (上傳時間) 3-Aug-2015 13:21:40 (UTC+8)-
dc.identifier (Other Identifiers) G0102352001en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/77182-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融研究所zh_TW
dc.description (描述) 102352001zh_TW
dc.description.abstract (摘要) 當保險契約被發行時，保險公司必須被要求盡可能的具備承擔未來不可知的風險的能力。本文將死亡風險、利率風險、脫退風險以及流動性風險引入，並針對生死合險契約進行盈餘分析。在此以 Vasicek (1977) 所提出之隨機利率模型、根據被保險人理性行為作為基礎之脫退模型以及引入簡化後的 Longstaff、Mithal與Nies (2005)流動性風險債券價格來描述各種風險。根據上述模型假設下計算保費及準備金，遂以蒙地卡羅模擬法量化源於各種風險之盈餘。最後，本文計算保險公司之盈餘對各風險參數之敏感度分析，並計算各期破產與發生流動性問題之可能性。zh_TW
dc.description.abstract (摘要) Once insurance contracts are issued, the insurers should be capable to deal with the unknown conditions in the future as possible. In this paper, we analyze the impact of mortality, interest rate, surrender and liquidity risks on the surplus of endowment contract. We model the interest rate risk by Vasicek model, the surrender rate based on the rational behavior of policyholders and introduce the discounted price of zero coupon bonds as the liquidity risk. Under such assumptions, we compute the premium and reserve, demonstrate the simulated insurance surplus, and finally exhibit the statistics of the surplus from different sources. The simulated results show the sensitivity of the surplus to the parameters of the risks. At the same time, we also show the probabilities of insolvency and illiquidity of the insurer before the maturity date of the contract due to the fluctuating surrender rate and liquidity risk resulting from the stochastic interest rate.en_US
dc.description.tableofcontents 1. Introduction 1
2. Endowment Contract 4
3. Assumptions for Models 6
3.1. Mortality Risk 6
3.2. Interest Rate Risk 6
3.3. Surrender Risk 8
3.4. Liquidity Risk 9
4. Premium and Reserve 11
4.1. Reserve Based on Assumed Interest Rate 11
4.2. Reserve and Premium 12
4.2.1. Case 1 12
4.2.2. Case 2 13
4.2.3. Case 3 14
5. Surplus Analysis 16
5.1. Surplus from Mortality Risk 18
5.2. Surplus from Interest Rate Risk 18
5.3. Surplus from Surrender Risk 19
5.4. Surplus from Liquidity Risk 19
5.5. Probability of Insolvency and Illiquidity 19
6. Numerical Illustrations 20
6.1. Sensitivity to Long-Term Interest Rate 20
6.2. Sensitivity to Volatility Parameter of Interest Rate 23
6.3. Sensitivity to Force of Reversion 25
6.4. Sensitivity to Parameter for Surrender Cash Value 28
6.5. Sensitivity to Parameter for Liquidity Risk 30
6.6. Sensitivity to Long-term Interest rate at Different Initial Interest rate 32
7. Conclusions 34
Appendices 35
A. Reserve Based on Assumed Interest Rate 35
B. Mortality Table 37
References 38		zh_TW
dc.format.extent 2866841 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102352001en_US
dc.subject (關鍵詞) 脫退zh_TW
dc.subject (關鍵詞) 隨機利率zh_TW
dc.subject (關鍵詞) 生死合險zh_TW
dc.subject (關鍵詞) 流動性風險zh_TW
dc.subject (關鍵詞) Surrenderen_US
dc.subject (關鍵詞) Stochastic Interest Rate Processen_US
dc.subject (關鍵詞) Endowment Contracten_US
dc.subject (關鍵詞) Liquidity Risken_US
dc.title (題名) 考量死亡、利率、脫退與流動性風險下生死合險契約之盈餘分析zh_TW
dc.title (題名) Surplus Analysis for Endowment Contracts Considering Mortality, Interest Rate, Surrender and Liquidity Risksen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Albizzati, M. O., Geman, H., 1994. Interest rate risk management and valuation of the surrender option in life Insurance policies. The Journal of Risk and Insurance. Vol. 61, 616-637.
[2] Bauer, D., Kiesel, R., Kling, A., Ruβ, J., 2006. Risk neutral valuation of participating life insurance contracts. Insurance: Mathematics and Economics. Vol. 39, 171-183.
[3] Berkowitz, J., 2000b. Incorporating liquidity risk into value-at-risk models. The Journal of Derivatives. Working Paper, University of California, Irvine.
[4] Brigo, D., Mercurio, F., 2007. Interest rate models: Theory and practice with smile, inflation and credit. Springer-Verlag Berlin Heidelberg.
[5] Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J., 1997. Actuarial mathematics. In: The Society of Actuaries. Itasca, Illinois.
[6] De Giovanni, 2010. Lapse rate modeling: A rational expectation approach. Scandinavian Actuarial Journal. Vol. 1, 56-68.
[7] Eling, M., Kiesenbauer, D., 2013. What policy features determine life insurance lapse? An analysis of the German market. The Journal of Risk and Insurance. Vol. 81, 241-269.
[8] Eling, M., Kochanski, M., 2012. Research on lapse in life insurance: What has been done and what needs to be done? The Journal of Risk Finance. Vol. 14, 392 –413.
[9] Fier, S., Liebenberg, A.P., 2013. Life insurance lapse behavior. North American Actuarial Journal. Vol. 17, 153-167.
[10] Geneva Association, 2012. Surrenders in the Life Insurance Industry and Their Impact on Liquidity.
[11] Kuo, W., Tsai, C., Chen, W., 2003. An empirical study on the lapse rate: The cointegration approach. The Journal of Risk and Insurance. Vol. 70, 487-508.
[12] Le Courtois, O., Nakagawa, H., 2011. On surrender and default risks. Mathematical Finance, forthcoming.
[13] Loisel, S., Milhaud, X., 2011. From deterministic to stochastic surrender risk models: Impact of correlation crises on economics capital. European Journal of Operational Research. Vol. 214, 348-357.
[14] Longstaff, F.A., Mithal, S., Neis, E., 2005. Corporate yield spreads: Default risk of liquidity? Now evidence from credit default swap market. The Journal of Finance. Vol. LX, 2213-2253.
[15] Nolde, N., Parker, G., 2014. Stochastic analysis of insurance surplus. Insurance Mathematics and Economics. Vol. 56, 1-13.
[16] Smink, M., 1991. Risk measurement for asset liability matching a simulation approach to single premium deferred annuities, 2nd AFIR International Colloquium. Brighton 1991. Proceedings, Vo1. 2, 75-92.
[17] Tsai, C., Kuo, W., Chiang, D. M.-H., 2009. The distributions of policy reserves considering the policy-year structures of surrender rates and expense ratios. Journal of Risk and Insurance. Vol. 76, 909-931.
[18] Vasicek, O., 1977. An equilibrium characterization of the term structure. Journal of Financial Economics. Vol. 5, 177-188.
[19] Zenios, S. A., 1999. Financial optimization. Cambridge University Press.		zh_TW