Publications-Theses

題名 隨機利率下分紅保單解約選擇權之評價分析
Fair Valuation of Participating Insurance Policies with Surrender Options
作者 張智凱
貢獻者 廖四郎<br>余清祥
<br>
張智凱
關鍵詞 分紅選擇權
解約選擇權
CRR 模型
公平價格
Participating option
Surrender option
CRR model
Fair value
日期 2005
上傳時間 17-Sep-2009 18:47:53 (UTC+8)
摘要 本文探討評價可解約分紅保單(Participating Policy)。該保單隱含二個重要的選擇權:分紅選擇權與解約選擇權。分紅選擇權為一歐式買權,解約選擇權可視為美式賣權。Bacinello(2003)使用CRR模型,計算解約選擇權的近似解,然而,Bacinello(2003)假設無風險利率為常數。本文主要探討如何利用無套利評價法,在隨機利率模型下,發展二維度之CRR模型,利用此模型,求得分紅選擇權與解約選擇權之公平價格,並討論利率的波動與長期走勢對該保單的選擇權的價格之影響。本文發現,保單之投資參考組合的波動,將對分紅選擇權的價格造成影響,而利率的波動會導致解約選擇權價格上升;當未來預期利率上升時,分紅選擇權與解約選擇權亦隨之上升。此評價模式可作為保險公司發行分紅保單與避險策略之參考。
Bacinello (2003a) employed Cox-Ross-Rubinstein model (CRR model, 1979) to numerically calculate the fair value of a participating policy containing a surrender option. Bacinello assumed a constant rate of return on risk-free assets. However, this study proposes a two-dimensional CRR model in a stochastic interest rate model as a means of providing a numerical method for contract pricing. The two-dimensional CRR model converges rapidly and achieves similar results to Monte Carlo simulation. Two-dimensional CRR models are used to analyze the importance and sensitivity of a stochastic interest rate model for the policy. Zero coupon bond volatility is an essential parameter in the surrender option, and reference portfolio volatility is important for pricing the participating option. The participating and surrender options are more valuable given upwards trending interest rates than constant or downwards trending rates.
參考文獻 Albizzati, M.-O., and Geman, H. (1994). Interest rate management and valuation of the surrender option in life insurance policies. Journal of Risk and Insurance, 61, 616-637.
Bacinello, A. R. (2001). Fair pricing of life insurance participating policies with a minimum interest rate guaranteed. Astin Bulletin, 31, 275-297.
Bacinello, A. R. (2003a). Fair valuation of a guaranteed life insurance participating contract embedding a surrender option. Journal of Risk and Insurance, 70, 461-487.
Bacinello, A. R. (2003b). Pricing guaranteed life insurance participating policies with annual premiums and surrender option. North American Actuarial Journal, 7, 1-17.
Bernard, C., Le Courtois, O., and Quittard-Pinon, F. (2005). Market value of life insurance contracts under stochastic interest rates and default risk. Insurance: Mathematics and Economics, 36, 499-516.
Black, F., and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-54.
Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., and Nesbitt, C. J. (1986). Actuarial mathematics. Society of Actuaries.
Boyle, P. P., and Schwartz, E. S. (1977). Equilibrium prices of guarantees under equity-linked contracts. Journal Risk and Insurance, 44, 639-60.
Brennan, M. J., and Schwartz, E. S. (1976). The pricing of equity-Linked life insurance policies with an asset value Guarantee. Journal of Financial Economics, 3, 195-213.
Brennan, M. J., and Schwartz, E. S. (1979a). Alternative investment strategies for the issues of equity-linked life insurance policies with an asset value guarantee. Journal of Business, 52, 63-93.
Brennan, M. J., and Schwartz, E. S. (1979b). Pricing and investment strategies for Equity-linked life insurance policies," Philadelpha: The S.S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania.
Briys, E., and de Varenne, F. (1994). Life insurance in a contingent claim framework: pricing and regulatory implications. The Geneva Papers on Risk and Insurance Theory, 19(1), 53-72.
Briys, E., and de Varenne, F. (1997a). On the risk of life insurance liabilities: debunking some common pitfalls. Journal of Risk and Insurance, 64, 673-694.
Briys, E., and de Varenne, F. (1997b). Valuing risky fixed rate debt: an extension. Journal of Financial Quantitative Analysis, 32(2), 239-248.
Cox, J. C., Ross, S. A., and Rubinstein, M. (1979). Option pricing: a simplified approach. Journal of Financial Economics, 7, 229-263.
Grosen, A., and J&oslash;rgensen, P. (1997). Valuation of early exercisable interest rate guarantees. Journal of Risk and Insurance, 64, 481-503.
Grosen, A., and J&oslash;rgensen, P. (2000). Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options, and bonus policies. Insurance: Mathematics and Economics, 26, 37-57.
Grosen, A., and J&oslash;rgensen, P. (2002). Life insurance liabilities at market value: an Analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework. Journal of Risk and Insurance, 69, 63-91.
Heath, D. C., Jarrow, R. A., and Morton, A. (1992). Bond pricing and the term structure
of interest rates: A new methodology for contingent claim valuation. Econometrica, 60,
77-105.
Ho, T. S. Y. and Lee, S. (1986). Term structure movements and pricing interest rate contingent claims. Journal of Finance, 41, 1011-1029.
Jensen, B., J&oslash;rgensen, P., and Grosen, A. (2001). A finite difference approach to the valuation of path dependent life insurance liabilities. The Geneva Papers on Risk and Insurance Theory, 26, 57-84.
J&oslash;rgensen, P. L., (2004). On Accounting Standards and Fair Valuation of Life Insurance and Pension Liabilities. Scand. Actuarial Journal 5, 372-394.
Longstaff, F. A. and Schwartz, E. S. (2001). Valuing American options by simulation: a simple least-square approach. The Review of Financial Studies, 14, 113-147.
Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics and
Management Science, 4, 141-183.
Miltersen, K., and Persson, S. (2003). Guaranteed investment contracts: distributed and undistributed excess return. Scandinavian Actuarial Journal, 4, 257-279.
Nielsen, J. A., and Sandmann, K. (1995). Equity-linked life insurance: a model with stochastic interest rates. Insurance: Mathematics and Economics, 16, 225-253.
Tanskanen, A., and Lukkarinen, J. (2003). Fair valuation of path-dependent participating life insurance contracts. Insurance: Mathematics and Economics, 33, 595-609.
Vasicek, O. (1977). An equilibrium characterization of term structure. Journal of Financial Economics, 5, 177-188.
描述 博士
國立政治大學
統計研究所
90354502
94
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0903545021
資料類型 thesis
dc.contributor.advisor 廖四郎<br>余清祥zh_TW
dc.contributor.advisor <br>en_US
dc.contributor.author (Authors) 張智凱zh_TW
dc.creator (作者) 張智凱zh_TW
dc.date (日期) 2005en_US
dc.date.accessioned 17-Sep-2009 18:47:53 (UTC+8)-
dc.date.available 17-Sep-2009 18:47:53 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 18:47:53 (UTC+8)-
dc.identifier (Other Identifiers) G0903545021en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/33914-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 90354502zh_TW
dc.description (描述) 94zh_TW
dc.description.abstract (摘要) 本文探討評價可解約分紅保單(Participating Policy)。該保單隱含二個重要的選擇權:分紅選擇權與解約選擇權。分紅選擇權為一歐式買權,解約選擇權可視為美式賣權。Bacinello(2003)使用CRR模型,計算解約選擇權的近似解,然而,Bacinello(2003)假設無風險利率為常數。本文主要探討如何利用無套利評價法,在隨機利率模型下,發展二維度之CRR模型,利用此模型,求得分紅選擇權與解約選擇權之公平價格,並討論利率的波動與長期走勢對該保單的選擇權的價格之影響。本文發現,保單之投資參考組合的波動,將對分紅選擇權的價格造成影響,而利率的波動會導致解約選擇權價格上升;當未來預期利率上升時,分紅選擇權與解約選擇權亦隨之上升。此評價模式可作為保險公司發行分紅保單與避險策略之參考。zh_TW
dc.description.abstract (摘要) Bacinello (2003a) employed Cox-Ross-Rubinstein model (CRR model, 1979) to numerically calculate the fair value of a participating policy containing a surrender option. Bacinello assumed a constant rate of return on risk-free assets. However, this study proposes a two-dimensional CRR model in a stochastic interest rate model as a means of providing a numerical method for contract pricing. The two-dimensional CRR model converges rapidly and achieves similar results to Monte Carlo simulation. Two-dimensional CRR models are used to analyze the importance and sensitivity of a stochastic interest rate model for the policy. Zero coupon bond volatility is an essential parameter in the surrender option, and reference portfolio volatility is important for pricing the participating option. The participating and surrender options are more valuable given upwards trending interest rates than constant or downwards trending rates.en_US
dc.description.tableofcontents 1. Introduction 1
2. Models 6
2.1 Contract Structurere 6
2.2 Stochastic Models 10
3. Two-dimensional CRR Models 14
3.1 Construction of Two-dimensional CRR Models 14
3.2 Valuation Framework 21
4. Numerical Analysis 25
4.1 Accuracy and Convergence 25
4.2 Sensitivity Analysis 32
5. Conclusions 37
References 39
Appendix 42
zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0903545021en_US
dc.subject (關鍵詞) 分紅選擇權zh_TW
dc.subject (關鍵詞) 解約選擇權zh_TW
dc.subject (關鍵詞) CRR 模型zh_TW
dc.subject (關鍵詞) 公平價格zh_TW
dc.subject (關鍵詞) Participating optionen_US
dc.subject (關鍵詞) Surrender optionen_US
dc.subject (關鍵詞) CRR modelen_US
dc.subject (關鍵詞) Fair valueen_US
dc.title (題名) 隨機利率下分紅保單解約選擇權之評價分析zh_TW
dc.title (題名) Fair Valuation of Participating Insurance Policies with Surrender Optionsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Albizzati, M.-O., and Geman, H. (1994). Interest rate management and valuation of the surrender option in life insurance policies. Journal of Risk and Insurance, 61, 616-637.zh_TW
dc.relation.reference (參考文獻) Bacinello, A. R. (2001). Fair pricing of life insurance participating policies with a minimum interest rate guaranteed. Astin Bulletin, 31, 275-297.zh_TW
dc.relation.reference (參考文獻) Bacinello, A. R. (2003a). Fair valuation of a guaranteed life insurance participating contract embedding a surrender option. Journal of Risk and Insurance, 70, 461-487.zh_TW
dc.relation.reference (參考文獻) Bacinello, A. R. (2003b). Pricing guaranteed life insurance participating policies with annual premiums and surrender option. North American Actuarial Journal, 7, 1-17.zh_TW
dc.relation.reference (參考文獻) Bernard, C., Le Courtois, O., and Quittard-Pinon, F. (2005). Market value of life insurance contracts under stochastic interest rates and default risk. Insurance: Mathematics and Economics, 36, 499-516.zh_TW
dc.relation.reference (參考文獻) Black, F., and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-54.zh_TW
dc.relation.reference (參考文獻) Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., and Nesbitt, C. J. (1986). Actuarial mathematics. Society of Actuaries.zh_TW
dc.relation.reference (參考文獻) Boyle, P. P., and Schwartz, E. S. (1977). Equilibrium prices of guarantees under equity-linked contracts. Journal Risk and Insurance, 44, 639-60.zh_TW
dc.relation.reference (參考文獻) Brennan, M. J., and Schwartz, E. S. (1976). The pricing of equity-Linked life insurance policies with an asset value Guarantee. Journal of Financial Economics, 3, 195-213.zh_TW
dc.relation.reference (參考文獻) Brennan, M. J., and Schwartz, E. S. (1979a). Alternative investment strategies for the issues of equity-linked life insurance policies with an asset value guarantee. Journal of Business, 52, 63-93.zh_TW
dc.relation.reference (參考文獻) Brennan, M. J., and Schwartz, E. S. (1979b). Pricing and investment strategies for Equity-linked life insurance policies," Philadelpha: The S.S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania.zh_TW
dc.relation.reference (參考文獻) Briys, E., and de Varenne, F. (1994). Life insurance in a contingent claim framework: pricing and regulatory implications. The Geneva Papers on Risk and Insurance Theory, 19(1), 53-72.zh_TW
dc.relation.reference (參考文獻) Briys, E., and de Varenne, F. (1997a). On the risk of life insurance liabilities: debunking some common pitfalls. Journal of Risk and Insurance, 64, 673-694.zh_TW
dc.relation.reference (參考文獻) Briys, E., and de Varenne, F. (1997b). Valuing risky fixed rate debt: an extension. Journal of Financial Quantitative Analysis, 32(2), 239-248.zh_TW
dc.relation.reference (參考文獻) Cox, J. C., Ross, S. A., and Rubinstein, M. (1979). Option pricing: a simplified approach. Journal of Financial Economics, 7, 229-263.zh_TW
dc.relation.reference (參考文獻) Grosen, A., and J&oslash;rgensen, P. (1997). Valuation of early exercisable interest rate guarantees. Journal of Risk and Insurance, 64, 481-503.zh_TW
dc.relation.reference (參考文獻) Grosen, A., and J&oslash;rgensen, P. (2000). Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options, and bonus policies. Insurance: Mathematics and Economics, 26, 37-57.zh_TW
dc.relation.reference (參考文獻) Grosen, A., and J&oslash;rgensen, P. (2002). Life insurance liabilities at market value: an Analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework. Journal of Risk and Insurance, 69, 63-91.zh_TW
dc.relation.reference (參考文獻) Heath, D. C., Jarrow, R. A., and Morton, A. (1992). Bond pricing and the term structurezh_TW
dc.relation.reference (參考文獻) of interest rates: A new methodology for contingent claim valuation. Econometrica, 60,zh_TW
dc.relation.reference (參考文獻) 77-105.zh_TW
dc.relation.reference (參考文獻) Ho, T. S. Y. and Lee, S. (1986). Term structure movements and pricing interest rate contingent claims. Journal of Finance, 41, 1011-1029.zh_TW
dc.relation.reference (參考文獻) Jensen, B., J&oslash;rgensen, P., and Grosen, A. (2001). A finite difference approach to the valuation of path dependent life insurance liabilities. The Geneva Papers on Risk and Insurance Theory, 26, 57-84.zh_TW
dc.relation.reference (參考文獻) J&oslash;rgensen, P. L., (2004). On Accounting Standards and Fair Valuation of Life Insurance and Pension Liabilities. Scand. Actuarial Journal 5, 372-394.zh_TW
dc.relation.reference (參考文獻) Longstaff, F. A. and Schwartz, E. S. (2001). Valuing American options by simulation: a simple least-square approach. The Review of Financial Studies, 14, 113-147.zh_TW
dc.relation.reference (參考文獻) Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics andzh_TW
dc.relation.reference (參考文獻) Management Science, 4, 141-183.zh_TW
dc.relation.reference (參考文獻) Miltersen, K., and Persson, S. (2003). Guaranteed investment contracts: distributed and undistributed excess return. Scandinavian Actuarial Journal, 4, 257-279.zh_TW
dc.relation.reference (參考文獻) Nielsen, J. A., and Sandmann, K. (1995). Equity-linked life insurance: a model with stochastic interest rates. Insurance: Mathematics and Economics, 16, 225-253.zh_TW
dc.relation.reference (參考文獻) Tanskanen, A., and Lukkarinen, J. (2003). Fair valuation of path-dependent participating life insurance contracts. Insurance: Mathematics and Economics, 33, 595-609.zh_TW
dc.relation.reference (參考文獻) Vasicek, O. (1977). An equilibrium characterization of term structure. Journal of Financial Economics, 5, 177-188.zh_TW