學術產出-Theses
Article View/Open
Publication Export
-
題名 一籃子違約交換評價之演算法改進
Improved algorithms for basket default swap valuation作者 詹依倫
Chan, Yi-Lun貢獻者 劉惠美
詹依倫
Chan, Yi-Lun關鍵詞 一籃子違約風險交換
多因子模型
Importance Sampling日期 2009 上傳時間 9-May-2016 15:11:22 (UTC+8) 摘要 各項信用衍生性商品中，最廣為人知的商品即為違約風險交換(credit default swap; CDS)，但由於金融市場與商品的擴張，標的資產不再侷限單一資產而是增加至數家或數百家，而多個標的資產的違約風險交換稱為一籃子違約風險交換(basket default swap; BDS)。 根據Chiang et al. ((2007), Journal of Derivatives, 8-19.)，在單因子模型中應用importance sampling (IS) 來估計違約給付金額，不僅可以確保違約事件的發生，還可以提高估計的效率，因此本文延伸此一概念，將此方法拓展至多因子模型。本文分為三種方法：一為將多個獨立因子合併為一邊際因子，並針對此邊際因子做importance sampling；二為找出其最具影響性的因子應用importance sampling；最後，我們針對portfolio C 於Glasserman ((2004), Journal of Derivatives, 24-42.) 將標的資產分為獨立兩群，我們將分段利用exponential twist及Chiang et al. (2007)所提出的單因子方法，提升違約事件發生的機率。 借由數值模擬結果，發現將多個獨立因子合併為一邊際因子的方法應用於標的資產為同質模型(homogeneous model)，會有較佳的結果；對具影響性的因子應用importance sampling的方法於各種模型之下的估計結果都頗為優秀，但其variance reduction較差且流程較不符合現實財務狀況，方法三則為特殊模型的應用，其只適用於能將標的資產獨立分群的模型，並且估計準確與否和選取exponential twist的位置有重要關係，第四節我們將同時呈現兩個不同位置的估計值與variance reduction.
Credit default swap (CDS) is the most popular in many kinds of credit derivatives, but number of obligor couldn’t be one always because of the expansions of financial market and contracts. CDS which has been contained more than one obligor is called basket default swap (BDS). According to Chiang et al. ((2007), Journal of Derivatives, 8-19.), applying importance sampling to estimate the default payment in one factor model could not only guarantee the default event occurs but also improve the efficiency of estimation. So this paper extends this concept for expanding this method to multiple factors model. There are three methods for expanding: First, merge multiple factors into a marginal factor and apply importance sampling to this marginal factor; second, apply importance sampling to the factor which has higher factor loading and third, we consider portfolio C in Glasserman ((2004), Journal of Derivatives, 24-42.) and divide total obligors into two independent groups. We would use the ways of exponential twist and the method in one factor model of Chiang et al. (2007) considered in two parts to raise the probability of default event occur. Borrow by the result of numerical simulation, method 1 has better results when obligors are homogeneous model; the results of method 2 are outstanding in each model, but its efficiency is worse and the procedure doesn’t fit with the realistic financial situation; the third method is the application of the special model, it could only apply to the model which could separate obligors independently, and the accuracy of estimates is strongly correlated to the position of exponential twist. In section 4, we would display the estimator and variance reduction in two different positions.參考文獻 1. Bassamboo, A., Juneja, S. and Zeevi, A (2008). “Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation.” Operations Research, Vol. 56, pp. 593-606. 2. Casella, G. and George, E.I. (1992) “Explaining the Gibbs Sampler.” The American Statistician, Vol. 46, pp. 167-174. 3. Chang, M.H., Yueh, M.L. and Hsieh, M.H. (2007). “An Efficient Algorithm for Basket Default Swap Valuation.” Journal of Derivatives, Vol. 15, pp. 8-19. 4. Embrechts, P., Lindskog, F. and McNeil, A. (2001). “Modelling Dependence with Copulas and Applications to Risk Management.” Working paper, Risklab ETH Zurich. 5. Glasserman, P. (2004). “Tail Approximations for Portfolio Credit Risk.” Journal of Derivatives, Vol. 12, pp. 24-42. 6. Glasserman, P. and Li, J. (2005). “Importance Sampling for Portfolio Credit Risk.” Journal of Management Science, Vol. 51, pp. 1643-1656. 7. Gould, H., Tobochnik, J. and Christian, W. (2006). An Introduction to Computer Simulation Methods. 3 edition, Addison Wesley. 8. Hull, J. and White, A. (2006). “Valuing Credit Derivatives Using an Implied Copula Approach.” Journal of Derivatives, Vol. 14, pp. 8-28. 9. Laurent, L.P. and Gregory, J. (2005). “Basket Default Swaps, CDO`s and Factor Copulas.” Journal of Risk, Vol. 7, pp.103-122.. 10. Li, D.X. (1998). “Constructing a Credit Curve.” Credit Risk, Special report on Credit Risk, pp. 40-44. …… (2000). “On Default Correlation: A Copula Function Approach.” Journal of Fixed Income, Vol. 9, pp. 43-54. 11. Lucas, A., Klaassen, P., Spreij, P. and Straetmans, S. (2003). “Tail behaviour of credit loss distributions for general latent factor models.” Applied Mathematical Finance, Vol. 10, pp. 337-357. 描述 碩士
國立政治大學
統計學系
96354006資料來源 http://thesis.lib.nccu.edu.tw/record/#G0096354006 資料類型 thesis dc.contributor.advisor 劉惠美 zh_TW dc.contributor.author (Authors) 詹依倫 zh_TW dc.contributor.author (Authors) Chan, Yi-Lun en_US dc.creator (作者) 詹依倫 zh_TW dc.creator (作者) Chan, Yi-Lun en_US dc.date (日期) 2009 en_US dc.date.accessioned 9-May-2016 15:11:22 (UTC+8) - dc.date.available 9-May-2016 15:11:22 (UTC+8) - dc.date.issued (上傳時間) 9-May-2016 15:11:22 (UTC+8) - dc.identifier (Other Identifiers) G0096354006 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/95117 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 96354006 zh_TW dc.description.abstract (摘要) 各項信用衍生性商品中，最廣為人知的商品即為違約風險交換(credit default swap; CDS)，但由於金融市場與商品的擴張，標的資產不再侷限單一資產而是增加至數家或數百家，而多個標的資產的違約風險交換稱為一籃子違約風險交換(basket default swap; BDS)。 根據Chiang et al. ((2007), Journal of Derivatives, 8-19.)，在單因子模型中應用importance sampling (IS) 來估計違約給付金額，不僅可以確保違約事件的發生，還可以提高估計的效率，因此本文延伸此一概念，將此方法拓展至多因子模型。本文分為三種方法：一為將多個獨立因子合併為一邊際因子，並針對此邊際因子做importance sampling；二為找出其最具影響性的因子應用importance sampling；最後，我們針對portfolio C 於Glasserman ((2004), Journal of Derivatives, 24-42.) 將標的資產分為獨立兩群，我們將分段利用exponential twist及Chiang et al. (2007)所提出的單因子方法，提升違約事件發生的機率。 借由數值模擬結果，發現將多個獨立因子合併為一邊際因子的方法應用於標的資產為同質模型(homogeneous model)，會有較佳的結果；對具影響性的因子應用importance sampling的方法於各種模型之下的估計結果都頗為優秀，但其variance reduction較差且流程較不符合現實財務狀況，方法三則為特殊模型的應用，其只適用於能將標的資產獨立分群的模型，並且估計準確與否和選取exponential twist的位置有重要關係，第四節我們將同時呈現兩個不同位置的估計值與variance reduction. zh_TW dc.description.abstract (摘要) Credit default swap (CDS) is the most popular in many kinds of credit derivatives, but number of obligor couldn’t be one always because of the expansions of financial market and contracts. CDS which has been contained more than one obligor is called basket default swap (BDS). According to Chiang et al. ((2007), Journal of Derivatives, 8-19.), applying importance sampling to estimate the default payment in one factor model could not only guarantee the default event occurs but also improve the efficiency of estimation. So this paper extends this concept for expanding this method to multiple factors model. There are three methods for expanding: First, merge multiple factors into a marginal factor and apply importance sampling to this marginal factor; second, apply importance sampling to the factor which has higher factor loading and third, we consider portfolio C in Glasserman ((2004), Journal of Derivatives, 24-42.) and divide total obligors into two independent groups. We would use the ways of exponential twist and the method in one factor model of Chiang et al. (2007) considered in two parts to raise the probability of default event occur. Borrow by the result of numerical simulation, method 1 has better results when obligors are homogeneous model; the results of method 2 are outstanding in each model, but its efficiency is worse and the procedure doesn’t fit with the realistic financial situation; the third method is the application of the special model, it could only apply to the model which could separate obligors independently, and the accuracy of estimates is strongly correlated to the position of exponential twist. In section 4, we would display the estimator and variance reduction in two different positions. en_US dc.description.tableofcontents 1. Introduction……………1 1.1 What’s Credit Default Swap (CDS)……………1 1.2 What’s Basket Default Swap (BDS)……………2 2. Literature Review……………4 2.1 Default time model and marginal default probability……………4 2.2 Copula Model……………6 2.3 Estimate the default payment of BDS in one factor model……………7 2.4 Estimate the default probability……………8 3. Multiple factors Algorithm for Basket Default Swap Valuation……………11 3.1 Combine multiple factors to marginal method……………11 3.2 Factor loading method……………13 3.3 Two way mixture method……………15 4. Numerical Results……………19 4.1 Model structure introduction……………19 4.2 Comparison of Simulation result……………20 5. Conclusion……………28 References……………29 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0096354006 en_US dc.subject (關鍵詞) 一籃子違約風險交換 zh_TW dc.subject (關鍵詞) 多因子模型 zh_TW dc.subject (關鍵詞) Importance Sampling en_US dc.title (題名) 一籃子違約交換評價之演算法改進 zh_TW dc.title (題名) Improved algorithms for basket default swap valuation en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 1. Bassamboo, A., Juneja, S. and Zeevi, A (2008). “Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation.” Operations Research, Vol. 56, pp. 593-606. 2. Casella, G. and George, E.I. (1992) “Explaining the Gibbs Sampler.” The American Statistician, Vol. 46, pp. 167-174. 3. Chang, M.H., Yueh, M.L. and Hsieh, M.H. (2007). “An Efficient Algorithm for Basket Default Swap Valuation.” Journal of Derivatives, Vol. 15, pp. 8-19. 4. Embrechts, P., Lindskog, F. and McNeil, A. (2001). “Modelling Dependence with Copulas and Applications to Risk Management.” Working paper, Risklab ETH Zurich. 5. Glasserman, P. (2004). “Tail Approximations for Portfolio Credit Risk.” Journal of Derivatives, Vol. 12, pp. 24-42. 6. Glasserman, P. and Li, J. (2005). “Importance Sampling for Portfolio Credit Risk.” Journal of Management Science, Vol. 51, pp. 1643-1656. 7. Gould, H., Tobochnik, J. and Christian, W. (2006). An Introduction to Computer Simulation Methods. 3 edition, Addison Wesley. 8. Hull, J. and White, A. (2006). “Valuing Credit Derivatives Using an Implied Copula Approach.” Journal of Derivatives, Vol. 14, pp. 8-28. 9. Laurent, L.P. and Gregory, J. (2005). “Basket Default Swaps, CDO`s and Factor Copulas.” Journal of Risk, Vol. 7, pp.103-122.. 10. Li, D.X. (1998). “Constructing a Credit Curve.” Credit Risk, Special report on Credit Risk, pp. 40-44. …… (2000). “On Default Correlation: A Copula Function Approach.” Journal of Fixed Income, Vol. 9, pp. 43-54. 11. Lucas, A., Klaassen, P., Spreij, P. and Straetmans, S. (2003). “Tail behaviour of credit loss distributions for general latent factor models.” Applied Mathematical Finance, Vol. 10, pp. 337-357. zh_TW
