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題名 以常態逆高斯分配評估一籃子信用違約交換之演算法
An Algorithm with the Normal Inverse Gaussian for Evaluating Basket Credit Default Swaps作者 吳秉霖 貢獻者 劉惠美
吳秉霖關鍵詞 一籃子信用違約交換
重要性取樣法
變異數縮減
單因子關聯結構
常態逆高斯分配
Basket credit default swaps
Importance sampling
Variance reduction
One factor copula
Normal inverse Gaussian日期 2012 上傳時間 2-九月-2013 15:37:18 (UTC+8) 摘要 由於信用衍生性商品近年來的蓬勃發展，與之相關的議題也越常提出來研究，本文就是以評價一籃子信用違約交換和估計投資組合損失機率為主，以單因子 關聯結構取代以往最常被應用的常態關聯結構，因最近許多研究表示，常態關聯結構並不能正確的表示出資產間的相關性。蒙地卡羅法為最常被應用在估計風險管理的工具，雖然有容易實行計算的優點，但是收斂速度緩慢卻是一大缺失，故本文以重要性取樣法來改善其收斂速度緩慢的缺點，但如果重要性密度函數選取的不好，也不能有效達到變異數縮減的效果，有時反而會有反效果的現象。所以本文藉由Chiang et al. (2007)所提出的重要性取樣法，此方法可保證必能達到變異數縮減，並將單因子 關聯結構模型套入此方法中，用以估計違約時之違約給付金額與投資組合損失機率大小，再以 分配中不同的參數與關聯結構中不同的共同因子權重等等因素，用模擬數值結果分析不同參數下對估計效率的影響，我們發現，在分配呈現偏態與共同因子權重越大時，估計的效率越好。
Recently, because of the prospered development of credit derivatives, the issues related to credit derivatives are more often discussed. The main purpose is to evaluate Basket Default Credit Swaps and estimate the probability of portfolio losses in the article. We use one factor Normal Inverse Gaussian copula to replace normal copula which is widely used in the past because normal copula cannot characterize the rela-tion between all dependent assets in many recent studies. Monte Carlo method is gen-erally used to estimate risk management. Although Monte Carlo method is easy to implement, converging slowly is its drawback. In this article, we improve the short-coming by the importance sampling procedure. But we cannot get efficient variance reduction and let it get the reverse effect if we choose an inappropriate probability density function of importance sampling. We use the importance sampling from the paper Chiang et al. published in 2007 and one factor NIG copula to estimate the de-fault leg and the probability of portfolio. The method can guarantee variance reduc-tion. By the simulate data from different parameters and common factor weight, fi-nally, we analysis the influence of estimated efficiency in various parameters. In con-clusion, the bigger the common factor weight is, the better the estimated efficiency is. Moreover, the efficiency is also better when NIG distribution is a skewed distribution.參考文獻 施明儒(2010)。評估極值相依組合信用風險之有效演算法。國立政治大學統計學研究所碩士論文。 Anderson, Eric C. (1999), “Monte Carlo Methods and Importance Sampling”, Lecture Notes for Stat 578C, Statistical Genetics Bassamboo, A., Juneja, S., and Zeevi, A.(2008), “Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation”, Operations Re-search,56(3),593-606 Chiang, M.H., Yueh, M.L., and Hsieh, M.H. (2007), “An Efficient Algorithm for Basket Default Swap Valuation”, Journal of Derivatives,15(2), David X. Li(2000), “On Default Correlation: A Copula Function Approach”, Journal of Fixed Income,9,43-54 Francis A. Longstaff and Rajan, A. (2008), “An Empirical Analysis of the Pricing of Collateralized Debt Obligations”, THE JOURNAL of FINANCE,VOL. LXIII, NO. 2 Glasserman, P. and Li, J.(2005), “Importance Sampling for Portfolio Credit Risk”, Management Science,51(11),1643-1656 Hull, J. and White, A.(2004), “Valuation of a CDO and an n-th to Default CDS With-out Monte Carlo Simulation”, Journal of Derivatives,12(2),8-23 Joshi, M.S. and Kainth, D. (2004), “Rapid and accurate development of prices and greeks for nth to default credit swaps in thr Li model”, Quantitative Finance, 4, 266-275. Kalemanova, A., Schmid, B., and Werner, R.(2007), “The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing”, Journal of Derivatives,14(3),80-94 Laurent, J. P. and Gregory, J.(2005), ” Basket Default Swaps, CODs and Factor Cop-ulas”, The Journal of Risk,7(4),103-122 Nan Chen, L. Jeff Hong(2007), “MONTE CARLO SIMULATION in FINANCIAL ENGINEERING”, Winter Simulation Conference Qiu Yue, Zhou Hong, and Wu Y.Q. (2007), “An Importance Sampling Method with Applications to Rare Event Probability”, IEEE International Conference on Grey Systems and Intelligent Services, November 18-20 描述 碩士
國立政治大學
統計研究所
100354027
101資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100354027 資料類型 thesis dc.contributor.advisor 劉惠美 zh_TW dc.contributor.author (作者) 吳秉霖 zh_TW dc.creator (作者) 吳秉霖 zh_TW dc.date (日期) 2012 en_US dc.date.accessioned 2-九月-2013 15:37:18 (UTC+8) - dc.date.available 2-九月-2013 15:37:18 (UTC+8) - dc.date.issued (上傳時間) 2-九月-2013 15:37:18 (UTC+8) - dc.identifier (其他 識別碼) G0100354027 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/59291 - dc.description (描述) 碩士 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) 100354027 zh_TW dc.description (描述) 101 zh_TW dc.description.abstract (摘要) 由於信用衍生性商品近年來的蓬勃發展，與之相關的議題也越常提出來研究，本文就是以評價一籃子信用違約交換和估計投資組合損失機率為主，以單因子 關聯結構取代以往最常被應用的常態關聯結構，因最近許多研究表示，常態關聯結構並不能正確的表示出資產間的相關性。蒙地卡羅法為最常被應用在估計風險管理的工具，雖然有容易實行計算的優點，但是收斂速度緩慢卻是一大缺失，故本文以重要性取樣法來改善其收斂速度緩慢的缺點，但如果重要性密度函數選取的不好，也不能有效達到變異數縮減的效果，有時反而會有反效果的現象。所以本文藉由Chiang et al. (2007)所提出的重要性取樣法，此方法可保證必能達到變異數縮減，並將單因子 關聯結構模型套入此方法中，用以估計違約時之違約給付金額與投資組合損失機率大小，再以 分配中不同的參數與關聯結構中不同的共同因子權重等等因素，用模擬數值結果分析不同參數下對估計效率的影響，我們發現，在分配呈現偏態與共同因子權重越大時，估計的效率越好。 zh_TW dc.description.abstract (摘要) Recently, because of the prospered development of credit derivatives, the issues related to credit derivatives are more often discussed. The main purpose is to evaluate Basket Default Credit Swaps and estimate the probability of portfolio losses in the article. We use one factor Normal Inverse Gaussian copula to replace normal copula which is widely used in the past because normal copula cannot characterize the rela-tion between all dependent assets in many recent studies. Monte Carlo method is gen-erally used to estimate risk management. Although Monte Carlo method is easy to implement, converging slowly is its drawback. In this article, we improve the short-coming by the importance sampling procedure. But we cannot get efficient variance reduction and let it get the reverse effect if we choose an inappropriate probability density function of importance sampling. We use the importance sampling from the paper Chiang et al. published in 2007 and one factor NIG copula to estimate the de-fault leg and the probability of portfolio. The method can guarantee variance reduc-tion. By the simulate data from different parameters and common factor weight, fi-nally, we analysis the influence of estimated efficiency in various parameters. In con-clusion, the bigger the common factor weight is, the better the estimated efficiency is. Moreover, the efficiency is also better when NIG distribution is a skewed distribution. en_US dc.description.tableofcontents 第一章 緒論...1 第二章 文獻探討...3 第三章 違約時間模型...5 3.1 存活函數和違約率函數...5 3.2 關聯結構函數...6 第四章 一籃子信用違約交換之評價...9 4.1 評價第k家標的物違約之一籃子信用違約交換...9 4.2 蒙地卡羅演算法...10 4.3 重要性取樣法...11 第五章 NIG關聯結構下評價一籃子信用違約交換...17 5.1 NIG分配與其特性...17 5.2 單因子NIG關聯結構模型...20 5.3 蒙地卡羅演算法－NIG...21 5.4 重要性取樣法－NIG...23 第六章 投資組合損失機率...26 6.1 蒙地卡羅演算法...26 6.2 重要性取樣演算法...28 第七章 數值模擬...31 7.1 一籃子信用違約交換之評價...31 7.2 投資組合損失機率...34 第八章 結論...36 參考文獻 ...37 附錄 ...39 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100354027 en_US dc.subject (關鍵詞) 一籃子信用違約交換 zh_TW dc.subject (關鍵詞) 重要性取樣法 zh_TW dc.subject (關鍵詞) 變異數縮減 zh_TW dc.subject (關鍵詞) 單因子關聯結構 zh_TW dc.subject (關鍵詞) 常態逆高斯分配 zh_TW dc.subject (關鍵詞) Basket credit default swaps en_US dc.subject (關鍵詞) Importance sampling en_US dc.subject (關鍵詞) Variance reduction en_US dc.subject (關鍵詞) One factor copula en_US dc.subject (關鍵詞) Normal inverse Gaussian en_US dc.title (題名) 以常態逆高斯分配評估一籃子信用違約交換之演算法 zh_TW dc.title (題名) An Algorithm with the Normal Inverse Gaussian for Evaluating Basket Credit Default Swaps en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 施明儒(2010)。評估極值相依組合信用風險之有效演算法。國立政治大學統計學研究所碩士論文。 Anderson, Eric C. (1999), “Monte Carlo Methods and Importance Sampling”, Lecture Notes for Stat 578C, Statistical Genetics Bassamboo, A., Juneja, S., and Zeevi, A.(2008), “Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation”, Operations Re-search,56(3),593-606 Chiang, M.H., Yueh, M.L., and Hsieh, M.H. (2007), “An Efficient Algorithm for Basket Default Swap Valuation”, Journal of Derivatives,15(2), David X. Li(2000), “On Default Correlation: A Copula Function Approach”, Journal of Fixed Income,9,43-54 Francis A. Longstaff and Rajan, A. (2008), “An Empirical Analysis of the Pricing of Collateralized Debt Obligations”, THE JOURNAL of FINANCE,VOL. LXIII, NO. 2 Glasserman, P. and Li, J.(2005), “Importance Sampling for Portfolio Credit Risk”, Management Science,51(11),1643-1656 Hull, J. and White, A.(2004), “Valuation of a CDO and an n-th to Default CDS With-out Monte Carlo Simulation”, Journal of Derivatives,12(2),8-23 Joshi, M.S. and Kainth, D. (2004), “Rapid and accurate development of prices and greeks for nth to default credit swaps in thr Li model”, Quantitative Finance, 4, 266-275. Kalemanova, A., Schmid, B., and Werner, R.(2007), “The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing”, Journal of Derivatives,14(3),80-94 Laurent, J. P. and Gregory, J.(2005), ” Basket Default Swaps, CODs and Factor Cop-ulas”, The Journal of Risk,7(4),103-122 Nan Chen, L. Jeff Hong(2007), “MONTE CARLO SIMULATION in FINANCIAL ENGINEERING”, Winter Simulation Conference Qiu Yue, Zhou Hong, and Wu Y.Q. (2007), “An Importance Sampling Method with Applications to Rare Event Probability”, IEEE International Conference on Grey Systems and Intelligent Services, November 18-20 zh_TW
