Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/137659


Title: 資產負債管理之研究分析
Essays on Asset and Liability Management Analysis
Authors: 宣葳
Hsuan, Wei
Contributors: 張士傑
Chang, Shih-Chieh
宣葳
Hsuan, Wei
Keywords: 利率變動型壽險
隨機變動模型
蒙地卡羅模擬
國際板債券
變額年金
copula-GARCH
Interest sensitive life insurance
Stochastic volatility
Monte-Carlo simulation
International bond
Variable annuities
Copula-GARCH
Date: 2021
Issue Date: 2021-11-01 11:54:32 (UTC+8)
Abstract: 本研究由三篇關於保險業資產負債管理議題的論文所構成。本文第二章檢視在台灣地區銷售之典型利率變動型壽險之公平定價問題。假設資產過程滿足Heston隨機變動模型、利率過程為CIR 模型,保險給付將為一系列遠期起點期權之總和。本文就台灣財務市場之資料進行模型參數估計,再利用蒙地卡羅法計算契約公平價格,同時計算風險值(VaR, ES)。本文第三章闡述國際板債券評價系統的實作細節。台灣保險業總資產近兩成之國際板債券在IFRS-9 會計準則下非為純債務工具,必須以公允價值衡量。在此我們敘述以美國固定期限公債收益率或美元LIBOR及ICE利率交換率校正的利率期限結構,配合芝加哥期貨交易所的歐式利率交換選擇權隱含波動度資料估計Hull-White 短期利率模型之評價理論細節,並使用開放原始碼程式語言Python 與函式庫QuantLib 及三元樹演算法實作國際板債券評價系統。除與櫃買中心系統價格輸出結果相比較外,我們展示本系統在給定利率期限結構與市場現有商品規格下可贖回債券期初價值與隱含年利率、不可贖回期間與可贖回頻率關係之計算。本文第四章探討copula-GARCH 模型在變額年金保證價值計算上的應用。有效的風險管理前提在於推估各種資產間的機率關係,並計算反映系統狀態的各種定量指標的能力。現代計算技術的進步使得更符合實際、不須過份簡化的多變量機率模型運用變為可能,而copula 正是如此的多變量機率模型。結合GARCH 時間序列模型,我們利用一系列基於無母數統計與經驗過程理論的穩健統計檢定方法,針對給定S&P500 與S&P600 指數時間序列選擇並匹配最適copula-GARCH 模型,進而推估變額年金保證價值。
This study focuses on the management of the three most challenging topics life insurers in Taiwan currently face, namely the life insurance policy with the highest annual
gross premium income, the dominating asset on the life insurer's balance sheet, and the development of a model which faithfully captures the dependency between multiple
underlying assets within the life insurer's portfolio. We first examine the fair pricing of interest rate sensitive life insurance policies that are commonly sold in Taiwan. With the reference portfolio following Heston's stochastic volatility process, the payoff function of these policies consists of a series of forward-start options. Although the option to surrender are standard features of these policies, policyholders incur heavy penalties should they exercise such option. Given certain policyholder behaviour, we study the impact of the minimum guaranteed interest rate, and the annually declared bonus rate on the issuing company's solvency. The need for pricing transparency and a reliable source of reference is of utmost importance in view of the sheer volume of the international bonds listed on the Taipei Exchange that the life insurers in Taiwan hold and the lack of a liquid secondary market. We provide the life insurers the means to evaluate the mark-to-market value of these callable bonds without having to rely on third parties to do so. We are able to collate publicly available data and make use of open source software to construct a bespoke system that can independently price the international bonds. The copula concept with its multivariate time-series model generalization, namely the copula-GARCH model, and robust statistical inference procedures based on the empirical processes theory are investigated in depth. A vast majority of existing literature on applications of copula often makes assumptions without justification or conducts inadequate statistical tests for verification. Here we demonstrate what we believed to be the preferred way of using copula for financial and risk management applications by the detailed valuation of guarantees embedded in variable annuities with multiple underlying assets.
Reference: Ametrano, F. M., & Bianchetti, M. (2013). Everything you always wanted to know about multiple interest rate curve bootstrapping but were afraid to ask. Social Science Research Network (SSRN) Working Paper Series. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2219548.
Andersen, L. (2008). Simple and efficient simulation of the Heston stochastic volatility model. Journal of Computational Finance, 11(3), 1–42.
Andersen, L., & Piterbarg, V. (2010a). Interest Rate Modeling. Volume I: Foundations and Vanilla Models. London: Atlantic Financial Press.
Andersen, L., & Piterbarg, V. (2010b). Interest Rate Modeling. Volume II: Term Structure Models. London: Atlantic Financial Press.
Andersen, L., & Piterbarg, V. (2010c). Interest Rate Modeling. Volume III: Products and Risk Management. London: Atlantic Financial Press.
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., & Ortu, F. (1996). Fixed income linked life insurance policies with minimum guarantees: Pricing models and numerical results. European Journal of Operatoinal Research, 91, 235–249.
Bai, J. (2003). Testing parametric conditional distributions of dynamic models. The Review of Economics and Statistics, 85(3), 531–549.
Bakshi, G., & Madan, P. (2000). Spanning and derivative-security valuation. Journal of Financial Economics, 55, 205–238.
Balaraman, G., & Ballabio, L. (2017). QuantLib Python Cookbook. Leanpub.
Ballabio, L. (2017). Implementing QuantLib. Leanpub.
Barbarin, J., & Devolder, P. (2005). Risk measure and fair valuation of an investment guarantee in life insurance. Insurance: Mathematics and Economics, 37(2), 297–323.
Bauer, D., Kiesel, R., Kling, A., & Ruß, J. (2006). Risk-neutral valuation of participating life insurance contracts. Insurance: Mathematics and Economics, 39(2), 171–183.
Bernard, C., Courtois, O. L., & Quittard-Pinon, F. (2006). Development and pricing of a new participating contract. North American Actuarial Journal, 10, 179–195.
Billingsley, P. (1999). Convergence of Probability Measures. New York: John Wiley & Sons, Second ed.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.
Blyth, S. (2014). An Introduction to Quantitative Finance. Oxford, UK: Oxford University Press.
Brennan, M. J., & Schwartz, E. S. (1976). The pricing of equity-linked life insurance policies with an asset value guarantee. Journal of Financial Economics, 3, 195–213.
Brigo, D., & Mercurio, F. (2006). Interest Rate Models – Theory and Practice: With Smile, Inflation and Credit. Berlin: Springer-Verlag, Second ed.
Briys, E., & 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., & de Varenne, F. (1997). On the risk of insurance liabilities: Debunking some common pitfalls. Journal of Risk and Insurance, 64(4), 673–694.
Chan, N.-H., Chen, J., Chen, X., Fan, Y., & Peng, L. (2009). Statistical inference for multivariate residual copula of GARCH models. Statistica Sinica, 19, 53–70.
Chang, S. C., & Wu, J. W. (2016). Risk assessment of international bond investment in Taiwan life insurance industry. Taiwan Insurance Review, 32(4), 1–33.
Chen, X., & Fan, Y. (2006a). Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. Journal of Econometrics, 135, 125–154.
Chen, X., & Fan, Y. (2006b). Estimation of copula-based semiparametric time series models. Journal of Econometrics, 130, 307–335.
Chiou, S.-C., & Tsay, R.-S. (2008). A copula-based approach to option pricing and risk assessment. Journal of Data Science, 6, 273–301.
Corb, H. (2012). Interest Rate Swaps and Other Derivatives. New York: Columbia University Press.
Cox, J., Ingersoll, J., & Ross, S. (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–407.
Da Fonseca, J., & Ziveyi, J. (2017). Valuing variable annuity guarantees on multiple assets. Scandinavian Actuarial Journal, 2017(3), 209–230.
Dai, T. S. (2017). The theoretical prices of USD zero-coupon callable international bonds are now available online. Taipei Exchange. URL https://nweb.tpex.org.tw/TPEX150/en/en_news2.html
Dickson, D., Hardy, M., & Waters, H. (2013). Actuarial Mathematics for Life Contingent Risks. Cambridge: Cambridge University Press, Second ed.
Dudley, R. (1999). Uniform Central Limit Theorem. Cambridge: Cambridge University Press.
Durante, F., & Sampi, C. (2016). Principles of Copula Theory. Boca Raton, F.L.: Chapman & Hall/CRC.
Fabozzi, F., & Mann, S. (2010). Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures, and Valuation. Hoboken, N.J.: John Wiley & Sons, Second ed.
Feller, W. (1951). Two singular diffusion problems. Annals of Mathematics, 54(1), 173–182.
Fermanian, J.-D., & Wegkamp, M. H. (2012). Time-dependent copulas. J. Multivariate Anal., 110, 19–29.
Gaenssler, P., & Stute, W. (1987). Seminar on Empirical Processes. Basel: Birkhaüser.
Gatzert, N., & Kling, A. (2007). Analysis of participating life insurance contracts: a unification approach. Journal of Risk and Insurance, 74(3), 547–570.
Gatzert, N., & Schmeiser, H. (2013). New life insurance financial products. In G. Dionne (Ed.) Handbook of Insurance, (pp. 1061–1095). Springer-Verlag, Second ed.
Genest, C., & Rémillard, B. (2004). Tests of independence and or randomness based on the empirical copula process. Test, 13, 335–369.
Genest, C., & Rémillard, B. (2008). Validity of the parametric bootstrap for goodness-of fit testing in semiparametric models. Ann. Inst. H. Poincarè Sect. B., 44, 1096–1127.
Ghalanos, A. (2018). rugarch: Univariate GARCH models. R package version 1.4-0. URL https://cran.r-project.org/web/packages/rugarch/index.html
Ghoudi, K., & Rémillard, B. (2014). Comparison of specification tests for GARCH models. Computational Statistics and Data Analysis, 76, 291–300.
Gilli, M., & Schumann, E. (2010). Calibrating option pricing models with heuristics. In A. Brabazon, M. O’Neill, & D. Maringer (Eds.) Natural Computing in Computational Finance: Volume 4, (pp. 9–37). New York: Springer-Verlag. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1566975.
Graf, S., Kling, A., & Ruß, J. (2011). Risk analysis and valuation of life insurance contracts: Combining actuarial and financial approaches. Insurance: Mathematics and Economics, 49, 115–125.
Graf, S., Kling, A., & Ruß, J. (2012). Financial planning and risk-return profiles. European Actuarial Journal, 2(1), 77–104.
Grosen, A., & Jørgensen, P. L. (1997). Valuation of early exercisable interest rate guarantees. Journal of Risk and Insurance, 64(3), 481–503.
Grosen, A., & Jørgensen, P. L. (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., & Jørgensen, P. L. (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.
Hayre, L. (Ed.) (2001). Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed Securities. New York: John Wiley & Sons.
Heston, S. (1993). A closed-form solutions for options with stochastic volatility. The Review of Financial Studies, 6, 327–343.
Hofert, M., Kojadinovic, I., Mächler, M., & Yan, J. (2017). copula: Multivariate Dependence with Copulas. R package version 0.999-18. URL http://cran.r-project.org/package=copula
Homer, S., Leibowitz, M. L., Bova, A., & Kogelman, S. (2013). Inside the Yield Book: The Classic That Created the Science of Bond Analysis. Hoboken, N.J.: John Wiley & Sons, Third ed.
Hsuan, W., & Chang, S. C. (2018a). The Copula-GARCH model: Application to variable annuity guarantee valuations on multiple assets. Journal of Risk Management, 20(2), 131–164.
Hsuan, W., & Chang, S. C. (2018b). Risk assessment of the life insurer in Taiwan: An examination of the interest sensitive life insurance policies. Journal of Risk Management, 20(1), 5–29.
Hsuan, W., & Chang, S. C. (2019). International bonds valuation system: Theory and practice. Taiwan Insurance Review, 35(3), 1–34.
Hull, J. C. (2018). Options, Futures, and Other Derivatives. Boston: Pearson, Tenth ed.
Hull, J. C., & White, A. (1990). Pricing interest rate derivative securities. The Review of Financial Studies, 3, 573–592.
Hull, J. C., & White, A. (1993a). Bond option pricing based on a model for the evolution of bond prices. Advances in Futures and Options Research, 6, 1–13.
Hull, J. C., & White, A. (1993b). Efficient procedures for valuing European and American path-dependent options. Journal of Derivatives, 1, 21–31.
Hull, J. C., & White, A. (1993c). One-factor interest rate models and the valuation of interest rate derivative securities. Journal of Financial and Quantitative Analysis,
28(2), 235–254.
Hull, J. C., & White, A. (1993d). The pricing of options on interest-rate caps and floors using the Hull-White model. The Journal of Financial Engineering, 2, 287–296.
Hull, J. C., & White, A. (1994a). Numerical procedures for implementing term structure models I: Single-factor models. Journal of Derivatives, 2, 7–16.
Hull, J. C., & White, A. (1994b). Numerical procedures for implementing term structure models II: Two-factor models. Journal of Derivatives, 2, 37–47.
Hull, J. C., & White, A. (1996). Using Hull-White interest rate trees. Journal of Derivatives, 3(3), 26–36.
Hull, J. C., & White, A. (2001). The general Hull-White model and supercalibration. Financial Analysts Journal, 57(6), 34–43.
Iacus, S. (2008). Simulation and Inference for Stochastic Differential Equations With R Examples. New York: Springer-Verlag.
Jamshidian, J. (1989). An exact bond option formula. Journal of Finance, 44(1), 205–209.
Jensen, B., Jørgensen, P. L., & 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.
Jha, S. (2011). Interest Rate Markets: A Practical Approach to Fixed Income. Hoboken, N.J.: John Wiley & Sons.
Joe, H. (2005). Asymptotic-efficiency of the two-stage estimation method for copula-based models. J. Multivariate Anal., 94, 401–419.
Joe, H. (2014). Dependence Modeling with Copulas. Boca Raton, F.L.: Chapman & Hall/CRC.
Jondeau, E., Poon, S. H., & Rockinger, M. (2007). Financial Modeling Under Non-Gaussian Distributions. Springer-Verlag.
Jondeau, E., & Rockinger, M. (2006). The copula-GARCH model of conditional dependencies: An international stock market application. Journal of International Money and Finance, 25(5), 827–853.
Kladıvko, K. (2007). Maximum likelihood estimation of the Cox-Ingersoll-Ross process: the MATLAB implementation. In Technical Computing Prague. working paper.
Kling, A., Richter, A., & Ruß, J. (2007). The interaction of guarantees, surplus distribution, and asset allocation in with-profit life insurance policies. Insurance: Mathematics and Economics, 40, 164–178.
Kojadinovic, I., & Yan, J. (2010). Modelling multivariate distributions with continuous margins using the copula r package. J. Statistical Software, 34(9).
Kosorok, M. (2008). Introduction to Empirical Processes and Semiparametric Inference. New York: Springer-Verlag.
Longstaff, F., & Schwartz, E. (2001). Valuing American options by simulation: A simple least squares approach. The Review of Financial Studies, 14(1), 113–147.
Miltersen, K. R., & Persson, S. A. (2003). Guaranteed investment contracts: distributed and undistributed excess return. Scandinavian Actuarial Journal, 4, 257–279.
Nasri, B., & Rémillard, B. (2018). Copula-based dynamic models for multivariate time series. Social Science Research Network (SSRN) Working Paper Series. URL https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3181605
Nasri, B. R., & Rémillard, B. N. (2019). Copula-based dynamic models for multivariate time series. J. Multivariate Anal., 172, 107–121.
Ng, C.-Y., & Li, S.-H. (2013). Pricing and hedging variable annuity guarantees with multiasset stochastic investment models. North American Actuarial Journal, 17(1), 41–62.
Patton, A. (2006). Modelling asymmetric exchange rate dependence. International Economic Review, 47, 527–556.
Price, K., Storn, R. M., & Lampinen, J. A. (2005). Differential Evolution: A Practical Approach to Global Optimization. New York: Springer-Verlag.
Rémillard, B. (2011). Validity of the parametric bootstrap for goodness-of-fit testing in dynamic models. Social Science Research Network (SSRN) Working Paper Series. URL https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1966476
Rémillard, B. (2012). Non-parametric change point problems using multipliers. Social Science Research Network (SSRN) Working Paper Series. URL https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2043632
Rémillard, B. (2013). Statistical Methods for Financial Engineering. Boca Raton, F.L.: Chapman & Hall/CRC.
Rémillard, B. (2017). Goodness-of-fit tests for copulas of multivariate time series. Econometrics, 5(1), 1–23.
Rosenberg, J. (1998). Pricing multivariate contingent claims using estimated risk-neutral density functions. Journal of International Money and Finance, 17, 229–247.
Rosenberg, J. (2003). Nonparametric pricing of multivariate contingent claims. Journal of Derivatives, 10, 9–26.
Rouah, F. (2013). The Heston Model and its Extensions in MATLAB and C#. Hoboken, N.J.: John Wiley & Sons.
Shorack, G., & Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. New York: John Wiley & Sons.
Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de L’Institut de Statistique de L’Université de Paris, 8, 229–231.
Storn, R., & Price, K. (1997). Differential evolution – a simple and efficient heuristic or global optimization over continuous spaces. Journal of Global Optimization, 11, 341–359.
Sundaresan, S. (2009). Fixed Income Markets and Their Derivatives. Burlington, MA: Academic Press, Third ed.
Tanskanen, A. J., & Lukkarinen, J. (2003). Fair valuation of path-dependent participating life insurance contracts. Insurance: Mathematics and Economics, 33, 595–609.
Tuckman, B., & Serrat, A. (2012). Fixed Income Securities: Tools for Today’s Markets. Hoboken, N.J.: John Wiley & Sons, Third ed.
van den Goorbergh, R., Genest, C., & Werker, B. (2005). Bivariate option pricing using dynamic copula models. Insurance: Mathematics and Economics, 37, 101–114.
van der Vaart, A. W., & Wellner, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. New York: Springer-Verlag.
van Haastrecht, A., Lord, R., Pelsser, A., & Schrager, R. (2009). Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility. Insurance: Mathematics and Economics, 45, 436–448.
Veronesi, P. (2010). Fixed Income Securities: Valuation, Risk, and Risk Management. Hoboken, N.J.: John Wiley & Sons.
Wilmott, P. (2002). Cliquet options and volatility models. Wilmott Magazine, December, 78–83.
Zhang, J., & Guégan, D. (2008). Pricing bivariate option under GARCH processes with time-varying copula. Insurance: Mathematics and Economics, 42, 1095–1103.
Description: 博士
國立政治大學
風險管理與保險學系
103358504
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0103358504
Data Type: thesis
Appears in Collections:[風險管理與保險學系 ] 學位論文

Files in This Item:

File Description SizeFormat
850401.pdf1356KbAdobe PDF8View/Open


All items in 學術集成 are protected by copyright, with all rights reserved.


社群 sharing