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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/124683
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/124683


    Title: 封閉偏斜常態因子模型違約風險估計之研究
    Estimating Tail Probability of Credit Loss Distribution with Closed Skew Normal
    Authors: 曹立諭
    Tsao, Li-Yu
    Contributors: 劉惠美
    Liu, Hui-Mei
    曹立諭
    Tsao, Li-Yu
    Keywords: 信用違約風險
    資產投資組合
    常態關聯結構
    封閉偏斜常態關聯結構
    蒙地卡羅法
    重要性取樣法
    指數轉換
    變異數縮減
    直尋牛頓法
    Normal-Copula
    Closed-Skew-Normal-Copula
    Asset Portfolio
    Credit Default Risk
    Monte Carlo Method
    Importance Sampling
    Exponential Twisting
    Variation Reduction
    Line Search Newton method
    Date: 2019
    Issue Date: 2019-08-07 16:01:25 (UTC+8)
    Abstract: 投資組合的信用風險常使用常態關聯結構模型進行估計,但模型能調整的參數有限,本篇使用封閉常態關聯結構模型進行推導,其分配擁有常態分配的性質,也具有調整分配偏度及厚尾程度的參數,使其更適合用在解釋投資組合間的相依程度。在衡量投資組合的稀有事件時,其機率值不易模擬,但卻包含著高額資產違約時的重大損失,若僅使用蒙地卡羅法模擬其信用風險,其模擬耗費的時間比一般事件還久且變異較大,我們使用Glasserman and Li (Management Science, 51(11), 1643-1656, 2005)與Chiang et al. (Journal of Derivatives, 15(2), 8-19, 2007)各別提出的重要性取樣法(簡稱GIS法與MIS法)進行推導及延伸,在封閉偏斜常態關聯結構模型的投資組合下進行模擬,透過變異數縮減效果衡量兩種方法的模擬效率。數值結果顯示,在單因子模型中,MIS法所花費的時間較GIS法少,其變異數縮減效果顯著;在多因子模型中,GIS法能適用的範圍較廣,透過兩階段重要性取樣法,其變異數縮減效果良好,模擬時間也較蒙地卡羅法縮短。兩種方法都有其適用的模型,也具有良好的估計精準度及模擬穩定性。
    The credit risk of the portfolio is often estimated using the Normal Copula model, but the parameters that the model can adjust are limited. This paper uses the Closed Normal Copula model to derive. The CSN distribution has the nature of normal distribution, and also has the adjustment distribution skewness. The degree of parameters make it more suitable for interpreting the degree of dependency between portfolios. When measuring the rare events of a portfolio, the probability value is not easy to simulate, but it contains a large loss in the event of a high-value Asset Default. Using Monte Carlo to simulate its credit risk, the simulation takes longer than usual and varies greatly. We use the importance sampling method proposed by Glasserman and Li (Management Science, 51(11), 1643-1656, 2005) and Chiang et al. (Journal of Derivatives, 15(2), 8-19, 2007). Referred to as GIS method and MIS method, it is deduced and extended. The simulation is carried out under the portfolio of Closed Skew Normal Copula model, and the simulation efficiency of the two methods is measured by the reduction effect of variance. The numerical results show that in the single factor model, the MIS method takes less time than the GIS method, and the Variance Reduction effect is significant. In the multi-factor model, the GIS method can be applied to a wide range, through the two-stage importance sampling method. The Variance Reduction effect is good, and the simulation time is shortened compared with the Monte Carlo method. Both methods have their applicable models and also have good estimation accuracy and simulation stability.
    Reference: [1] 邱嬿燁 (2008).“探討單因子複合分配關聯結構模型之擔保債權憑證之評價”,國立政治大學統計學系碩士論文.
    [2] 陳家丞 (2016).“極值相依模型下投資組合之重要性取樣法”,國立政治大學統計學系碩士論文.
    [3] 許文銘 (2016).“異質性投資組合下的改良式重點取樣法”,國立政治大學統計學系碩士論文.
    [4] Azzalini, A. (1985). “A class of distributions which includes the normal ones.”, Scandinavian Journal of Statistics, 171-178.
    [5] Azzalini, A. (2005). “The Skew-normal Distribution and Related Multivariate
    Families.”, Scandinavian Journal of Statistics, 32(2), 159-188.
    [6] Azzalini A. and Dalla-Valle A. (1996). “The multivariate skew-normal distribution.”, Biometrika, 83(4), 715–726.
    [7] Chiang, M.H., Yueh, M.L., and Hsieh, M.H. (2007). “An Efficient Algorithm for
    Basket Default Swap Valuation.”, Journal of Derivatives, 15(2), 8-19.
    [8] Elal-Olivero, D. (2010). “ Alpha-skew-normal distribution. ” Proyecciones
    (Antofagasta), 29(3), 224-240.
    [9] Glasserman‚ P. (2004). “Tail Approximations for Portfolio Credit Risk.”‚ Journal of Derivatives, 12(2), 24-42.
    [10] Glasserman, P. and Li, J. (2005). “Importance Sampling for Portfolio Credit Risk.”, Management Science, 51(11),1643-1656.
    [11] Glasserman, P., Heidelberger, P. and Shahabuddin, P. (2000). “Variance Reduction Techniques for Estimating Value-at-Risk. ”, Management Science, 46(10), 1349-1364.
    [12] González-Farías, G., Domínguez-Molina, J.A. and Gupta, A.K. (2004). “Additive properties of skew normal random vectors.”, Journal of Statistical Planning and Inference, 126(2), 521-534.
    [13] González-Farías, G., Domínguez-Molina, J.A. and Gupta, A.K. (2004). “A
    multivariate skew normal distribution.”, Journal of Multivariate Analysis, 89(1), 181-190.
    [14] Han, C.H, and Wu, C.T. (2010). “Efficient importance sampling for estimating
    lower tail probabilities under Gaussian and Student’s t distributions.”, Preprint.
    National Tsing-Hua University.
    [15] Li, D.X. (1999). “On default correlation: a copula function approach.” , Journal of Fixed Income , 9(4), 43-54.
    [16] Nocedal, J., and M. Wright. (1999). Numerical Optimization. Springer-Verlag, New York.
    [17] Wilson, T. (1999). “Value at risk. ” Risk Management and Analysis, 1, 61-124.
    Description: 碩士
    國立政治大學
    統計學系
    106354012
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0106354012
    Data Type: thesis
    DOI: 10.6814/NCCU201900228
    Appears in Collections:[統計學系] 學位論文

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