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題名 壽險業系統性風險與清償能力評估之研究
Research on the Systematic Risk and Solvency Assessment in Life Insurance Market
作者 朱柏璁
Chu, Po Tsung
貢獻者 張士傑
Chang, Shih Chieh
朱柏璁
Chu, Po Tsung
關鍵詞 隨機波動模型
系統性風險
違約價值
stochastic volatility
systematic risk
default value
日期 2015
上傳時間 3-Aug-2015 13:23:07 (UTC+8)
摘要 此研究主要研究壽險業的系統性風險與違約風險之評價，基於投資組合的波動度去建立隨機過程模型。特別是那些隱含無法被多角化的財務風險、系統性風險，透過研究，使用Heston(1993)模型去描述標的資產的隨機波動程度比以往使用Black-Scholes(1973)模型描述股價的波動變化更能反映實際的風險狀況，並透過CIR過程來表示瞬間的波動程度。在這個模型之中，把過去以平賭測度決定違約選擇權的方法延伸。此外透過探討違約價值之敏感度，根據不同的情境測試對於壽險公司負債的影響。最後透過數值的結果與敏感度分析隨機波動模型與確定性的模型之差異。
當資本準備增加時，資產與負債比提高，因負債仍固定承諾予保戶之利率增長，而資產因應系統性風險的發生而減損仍能支付負債，致使違約風險降低，進而使得評價時點的違約金額降低。當系統風險發生時，風險值上升，違約價值為右偏分布，代表在極端條件下有可能有極大的損失；反之，當整個金融體系經濟情勢良好，公司擁有足夠的經濟資本時，風險值下降，滿足VaR75與CTE65的法規限制，此時公司的清償能力足以反映系統性風險。
This paper considers the problem of valuating the default option of the life insurers that are subject to systematic financial risk in the sense that the volatility of the investment portfolio is modeled through stochastic processes. In particular, this implies that the financial risk cannot be eliminated through diversifying the asset portfolio. In our work, Heston (1993) model is employed in describing the evolution of the volatility of an underlying asset, while the instantaneous variance is a CIR process. Within this model, we study a general set of equivalent martingale measures, and determine the default option by applying these measures. In addition, we investigate the sensitivity of the default values given regulatory forbearance for the life insurance liabilities considered. Numerical examples are included, and the use of the stochastic volatility model is compared with deterministic models.
As reserve of capital is increasing, asset-liability ratio is also increasing. The liability grew up with promised interest rate, and it could be covered by the asset when the systematic risk events happened. Therefore, the default risk was decreasing, that caused the default value decreasing. When the systematic risk events happened, the value of risk was increasing, and the default value was positive skew distribution. That means the maximum loss will be coming in the extreme case. On the other hand, when prosperity economy occurred, the value of risk was decreasing, which in compliance with the law of VaR75&CTE65 rules, and the insurance company had enough capital to face the systematic risk events.
參考文獻 1. J. Barbarin, P. Devolder, (2005), Risk measure and fair valuation of an investment guarantee in life insurance, Insurance: Mathematics and Economics 37,297-323.
2. Billio, M. and M. Getmansky, (2010), Measuring Systemic Risk in the Finance and Insurance Sector, MIT Sloan School Working Paper.
3. Chang, S.C. , (1999), Optimal Pension Funding through Dynamic Simulations : the Case of Taiwan Public Employees Retirement System, Insurance: Mathematics and Economics 24,187-199.
4. Han, C.H., Liu, W.H. and Chen, Z.Y., (2013), VaR/CVaR Estimation under Stochastic Volatility Models, International Journal of Theoretical and Applied Finance 17,35-86.
5. Cummins, J.D., Harrington, S.E., Klein, R. , (1995), Insolvency Experience, Risk-Based Capital, and Prompt Corrective Action in Property-Liability Insurance, Journal of Banking and Finance 19, 511-527.
6. Duan, J.C. and Yu, M.T. , (1994), Forbearance and Pricing Deposit Insurance in a 32 Multiperiod Framework, Journal of Risk and Insurance 61, 575-591.
7. Etti G. Baranoff and Thomas W. Sager, (2002), The Relations among Asset Risk, Product risk, and Capital in the life insurance industry, Journal of Banking & Finance 26, 1181-1197
8. Heath, D., Jarrow, R., and Morton, A., (1992), Bond Pricing and the Term of Interest Rates: A New Methodology for Contingent Claims Valuation. Journal of the Econometric Society 60, 77-105.
9. Helwege, J., (2009), Financial Firm Bankruptcy and Systemic Risk, Regulation, 32(2), 24-29.
10. Heston, Steven L., (1993), A closed-form solutions for options with stochastic volatility, Reviewof Financial Studies 6, 327–343.
11. Huberto M.E.s and H.S. Malek, (2005), Bank risk of failure and the too-big-to-fail policy, Economic Quarterly, Federal Reserve Bank of Richmond, 91(2), 21-44.
12. Hato Schmeiser, (2008) ,The United States RBC Standards, Solvency II, and the Swiss Solvency Test: A Comparative Assessment, Geneva Papers 34, 56-77.
13. J. Yu, H. Skaug, (2009), Stimulated Maximum Likelihood Estimation of Continuous Time Stochastic Volatility Models, Singapore Management University working paper.
14. Kevin Jacques and Peter Nigro , (1994),Risk-Based Capital, Portfolio Risk, and Bank Capital: A Simultaneous Equations Approach, Journal of Economics and Business 49, 533-547.
15. Kevin Dowd and David Blake, (2006), After VAR: The Theory, Estimation, and Insurance Applications of Quantile-based Risk Measures, The Journal of Risk and Insurance 73, 193-229.
16. S. L. Heston, (1993), A Close-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Review of Financial Studies 6, 327-343.
17. Stewart C. Myers James A. Read, Jr, (2001), Capital Allocation for Insurance Companies, The Journal of Risk and Insurance 68, 545-580.
18. Tsai, C., W. K. Chen, and C. Chan (2003), On the Distribution of Life Insurance Reserves in a Stochastic Mortality, Interest Rate, and Surrender Rate Environment, Review of Securities and Futures Markets 58, 1–30.
19. Tsai, C., W. Kuo, and D. Chiang (2009), The Distributions of Policy Reserves Considering the Policy-Year Structures of Surrender Rates and Expense Ratios,Journal of Risk and Insurance 76, 909–931.
20. Nimalin Moodley, (2005) The Heston Model:A Practical Approach with Matlab Code.
21. Mikkel Dahl, Thomas Møller (2006), Valuation and hedging of life insurance liabilities with systematic mortality risk, Insurance: Mathematics and Economics 39, 193–217.
22. Martin Eling, Hato Schmeiser and Joan T. Schmit , (2006),The Solvency II Process: Overview and Critical analysis, Risk Management and Insurance Review 10, 69-85.
23. Merton, R.C. , (1977), An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantee. Journal of Banking and Finance 1, 3-11.
24. Monica Billio, Mila Getmansky,(2012), Econometric measures of connectedness and systemic risk in the finance and insurance sectors, Journal of Financial Economics 104, 535-599.
25. Nimalin Moodley, (2005), The Heston Model: A Practical Approach with Matlab Code, Programme in Advanced Mathematics of Finance, Bachelor of Science Honours.
26. Pottier, S. W. and D. W. Sommer, (2002), The Effectiveness of Public and Private Sector Summary Risk Measures in Predicting Insurer Insolvencies, Journal of Finance Services Research 21, 101-116.
27. 張士傑、黃雅文，(2010)。《保險業資產配置之決定及其影響》。出版地：財團法人保險安定基金、中華民國風險管理學會。
28. 謝明華、黃雅文、郭維裕、蔡政憲，(2014)。《壽險準備金風險》。出版地：中央研究院經濟研究所。
描述 碩士
國立政治大學
風險管理與保險研究所
102358009
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102358009
資料類型 thesis
dc.contributor.advisor 張士傑zh_TW
dc.contributor.advisor Chang, Shih Chiehen_US
dc.contributor.author (Authors) 朱柏璁zh_TW
dc.contributor.author (Authors) Chu, Po Tsungen_US
dc.creator (作者) 朱柏璁zh_TW
dc.creator (作者) Chu, Po Tsungen_US
dc.date (日期) 2015en_US
dc.date.accessioned 3-Aug-2015 13:23:07 (UTC+8)-
dc.date.available 3-Aug-2015 13:23:07 (UTC+8)-
dc.date.issued (上傳時間) 3-Aug-2015 13:23:07 (UTC+8)-
dc.identifier (Other Identifiers) G0102358009en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/77190-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 102358009zh_TW
dc.description.abstract (摘要) 此研究主要研究壽險業的系統性風險與違約風險之評價，基於投資組合的波動度去建立隨機過程模型。特別是那些隱含無法被多角化的財務風險、系統性風險，透過研究，使用Heston(1993)模型去描述標的資產的隨機波動程度比以往使用Black-Scholes(1973)模型描述股價的波動變化更能反映實際的風險狀況，並透過CIR過程來表示瞬間的波動程度。在這個模型之中，把過去以平賭測度決定違約選擇權的方法延伸。此外透過探討違約價值之敏感度，根據不同的情境測試對於壽險公司負債的影響。最後透過數值的結果與敏感度分析隨機波動模型與確定性的模型之差異。
當資本準備增加時，資產與負債比提高，因負債仍固定承諾予保戶之利率增長，而資產因應系統性風險的發生而減損仍能支付負債，致使違約風險降低，進而使得評價時點的違約金額降低。當系統風險發生時，風險值上升，違約價值為右偏分布，代表在極端條件下有可能有極大的損失；反之，當整個金融體系經濟情勢良好，公司擁有足夠的經濟資本時，風險值下降，滿足VaR75與CTE65的法規限制，此時公司的清償能力足以反映系統性風險。		zh_TW
dc.description.abstract (摘要) This paper considers the problem of valuating the default option of the life insurers that are subject to systematic financial risk in the sense that the volatility of the investment portfolio is modeled through stochastic processes. In particular, this implies that the financial risk cannot be eliminated through diversifying the asset portfolio. In our work, Heston (1993) model is employed in describing the evolution of the volatility of an underlying asset, while the instantaneous variance is a CIR process. Within this model, we study a general set of equivalent martingale measures, and determine the default option by applying these measures. In addition, we investigate the sensitivity of the default values given regulatory forbearance for the life insurance liabilities considered. Numerical examples are included, and the use of the stochastic volatility model is compared with deterministic models.
As reserve of capital is increasing, asset-liability ratio is also increasing. The liability grew up with promised interest rate, and it could be covered by the asset when the systematic risk events happened. Therefore, the default risk was decreasing, that caused the default value decreasing. When the systematic risk events happened, the value of risk was increasing, and the default value was positive skew distribution. That means the maximum loss will be coming in the extreme case. On the other hand, when prosperity economy occurred, the value of risk was decreasing, which in compliance with the law of VaR75&CTE65 rules, and the insurance company had enough capital to face the systematic risk events.		en_US
dc.description.tableofcontents 第一章 緒論 7
第一節 研究動機與目的 7
第二節 文獻回顧 9
第二章 系統性風險與清償能力評估 11
第一節 壽險業系統性風險 11
第二節 資本清償能力(RBC) 13
第三節 Solvency II 歐洲保險清償能力監理 15
第四節 系統性風險估計與測量方法 18
第三章 經濟資本與模型假設 19
第一節 違約價值之評價 19
第二節 Heston(1993)評價模型 21
第三節 Heston 模型與參數估計 24
第四節 資產負債模型 27
第四章 數值分析 30
第一節 模擬方法 30
第二節 參數估計 32
第三節 數值結果 34
第五章 結論與建議 38
參考文獻 40
附錄 44		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102358009en_US
dc.subject (關鍵詞) 隨機波動模型zh_TW
dc.subject (關鍵詞) 系統性風險zh_TW
dc.subject (關鍵詞) 違約價值zh_TW
dc.subject (關鍵詞) stochastic volatilityen_US
dc.subject (關鍵詞) systematic risken_US
dc.subject (關鍵詞) default valueen_US
dc.title (題名) 壽險業系統性風險與清償能力評估之研究zh_TW
dc.title (題名) Research on the Systematic Risk and Solvency Assessment in Life Insurance Marketen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. J. Barbarin, P. Devolder, (2005), Risk measure and fair valuation of an investment guarantee in life insurance, Insurance: Mathematics and Economics 37,297-323.
2. Billio, M. and M. Getmansky, (2010), Measuring Systemic Risk in the Finance and Insurance Sector, MIT Sloan School Working Paper.
3. Chang, S.C. , (1999), Optimal Pension Funding through Dynamic Simulations : the Case of Taiwan Public Employees Retirement System, Insurance: Mathematics and Economics 24,187-199.
4. Han, C.H., Liu, W.H. and Chen, Z.Y., (2013), VaR/CVaR Estimation under Stochastic Volatility Models, International Journal of Theoretical and Applied Finance 17,35-86.
5. Cummins, J.D., Harrington, S.E., Klein, R. , (1995), Insolvency Experience, Risk-Based Capital, and Prompt Corrective Action in Property-Liability Insurance, Journal of Banking and Finance 19, 511-527.
6. Duan, J.C. and Yu, M.T. , (1994), Forbearance and Pricing Deposit Insurance in a 32 Multiperiod Framework, Journal of Risk and Insurance 61, 575-591.
7. Etti G. Baranoff and Thomas W. Sager, (2002), The Relations among Asset Risk, Product risk, and Capital in the life insurance industry, Journal of Banking & Finance 26, 1181-1197
8. Heath, D., Jarrow, R., and Morton, A., (1992), Bond Pricing and the Term of Interest Rates: A New Methodology for Contingent Claims Valuation. Journal of the Econometric Society 60, 77-105.
9. Helwege, J., (2009), Financial Firm Bankruptcy and Systemic Risk, Regulation, 32(2), 24-29.
10. Heston, Steven L., (1993), A closed-form solutions for options with stochastic volatility, Reviewof Financial Studies 6, 327–343.
11. Huberto M.E.s and H.S. Malek, (2005), Bank risk of failure and the too-big-to-fail policy, Economic Quarterly, Federal Reserve Bank of Richmond, 91(2), 21-44.
12. Hato Schmeiser, (2008) ,The United States RBC Standards, Solvency II, and the Swiss Solvency Test: A Comparative Assessment, Geneva Papers 34, 56-77.
13. J. Yu, H. Skaug, (2009), Stimulated Maximum Likelihood Estimation of Continuous Time Stochastic Volatility Models, Singapore Management University working paper.
14. Kevin Jacques and Peter Nigro , (1994),Risk-Based Capital, Portfolio Risk, and Bank Capital: A Simultaneous Equations Approach, Journal of Economics and Business 49, 533-547.
15. Kevin Dowd and David Blake, (2006), After VAR: The Theory, Estimation, and Insurance Applications of Quantile-based Risk Measures, The Journal of Risk and Insurance 73, 193-229.
16. S. L. Heston, (1993), A Close-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Review of Financial Studies 6, 327-343.
17. Stewart C. Myers James A. Read, Jr, (2001), Capital Allocation for Insurance Companies, The Journal of Risk and Insurance 68, 545-580.
18. Tsai, C., W. K. Chen, and C. Chan (2003), On the Distribution of Life Insurance Reserves in a Stochastic Mortality, Interest Rate, and Surrender Rate Environment, Review of Securities and Futures Markets 58, 1–30.
19. Tsai, C., W. Kuo, and D. Chiang (2009), The Distributions of Policy Reserves Considering the Policy-Year Structures of Surrender Rates and Expense Ratios,Journal of Risk and Insurance 76, 909–931.
20. Nimalin Moodley, (2005) The Heston Model:A Practical Approach with Matlab Code.
21. Mikkel Dahl, Thomas Møller (2006), Valuation and hedging of life insurance liabilities with systematic mortality risk, Insurance: Mathematics and Economics 39, 193–217.
22. Martin Eling, Hato Schmeiser and Joan T. Schmit , (2006),The Solvency II Process: Overview and Critical analysis, Risk Management and Insurance Review 10, 69-85.
23. Merton, R.C. , (1977), An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantee. Journal of Banking and Finance 1, 3-11.
24. Monica Billio, Mila Getmansky,(2012), Econometric measures of connectedness and systemic risk in the finance and insurance sectors, Journal of Financial Economics 104, 535-599.
25. Nimalin Moodley, (2005), The Heston Model: A Practical Approach with Matlab Code, Programme in Advanced Mathematics of Finance, Bachelor of Science Honours.
26. Pottier, S. W. and D. W. Sommer, (2002), The Effectiveness of Public and Private Sector Summary Risk Measures in Predicting Insurer Insolvencies, Journal of Finance Services Research 21, 101-116.
27. 張士傑、黃雅文，(2010)。《保險業資產配置之決定及其影響》。出版地：財團法人保險安定基金、中華民國風險管理學會。
28. 謝明華、黃雅文、郭維裕、蔡政憲，(2014)。《壽險準備金風險》。出版地：中央研究院經濟研究所。		zh_TW