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題名 評估極值相依組合信用風險之有效演算法
Efficient Algorithms for Evaluating Portfolio Credit Risk with Extremal Dependence
作者 施明儒
Shih,Ming Ju
貢獻者 劉惠美<br>陳麗霞
Liu,Huimei<br>Chen,Li Shya
施明儒
Shih,Ming Ju
關鍵詞 蒙地卡羅法
組合信用風險
t 關聯結構
極值相依
一籃子信用違約交換
重要性取樣
變異數縮減
Monte Carlo method
Portfolio credit risk
t-copula
Extremal dependence
Basket credit default swaps
Importance sampling
Variance reduction
日期 2009
上傳時間 5-Sep-2013 15:10:22 (UTC+8)
摘要 蒙地卡羅模擬是在組合信用風險的管理上相當實用的計算工具。衡量組合信用風險時，必須以適當的模型描述資產間的相依性。常態關聯結構是目前最廣為使用的模型，但實證研究認為 t 關聯結構更適合用於配適金融市場的資料。在本文中，我們採用 Bassamboo et al. (2008) 提出的極值相依模型建立 t 關聯結構用以捕捉資產之間的相關性。同時，為增進蒙地卡羅法之收斂速度，我們以 Chiang et al. (2007) 的重要性取樣法為基礎，將其拓展到極值相依模型下，並提出兩階段的重要性取樣技巧確保使用此方法估計一籃子信用違約時，所有模擬路徑均會發生信用事件。數值結果顯示，所提出的演算法皆達變異數縮減。而在模型自由度較低或是資產池較大的情況下，兩階段的重要性取樣法將會有更佳的估計效率。我們也以同樣的思路，提出用以估計投資組合損失機率的演算法。雖然所提出的演算法經過重要性取樣的技巧後仍無法使得欲估計的事件在所有模擬路徑下都會發生，但數值結果仍顯示所提出的方法估計效率遠遠優於傳統蒙地卡羅法。
Monte Carlo simulation is a useful tool on portfolio credit risk management. When measuring portfolio credit risk, one should choose an appropriate model to characterize the dependence among all assets. Normal copula is the most widely used mechanism to capture this dependence structure, however, some emperical studies suggest that $t$-copula provides a better fit to market data than normal copula does. In this article, we use extremal depence model proposed by Bassamboo et al. (2008) to construct $t$-copula. We also extend the importance sampling (IS) procedure proposed by Chiang et al. (2007) to evaluate basket credit default swaps (BDS) with extremal dependence and introduce a two-step IS algorithm which ensures credit events always take place for every simulation path. Numerical results show that the proposed methods achieve variance reduction. If the model has lower degree of freedom, or the portfolio size is larger, the two-step IS method is more efficient. Following the same idea, we also propose algorithms to estimate the probability of portfolio losses. Althought the desired events may not occur for some simulations, even if the IS technique is applied, numerical results still show that the proposed method is much better than crude Monte Carlo.
參考文獻 Bassamboo, A., Juneja, S., and Zeevi, A. (2008), Portfolio credit risk
with extremal dependence: Asymptotic analysis and efficient simulation,
Operations Research, 56(3), 593--606.

Bruyere, R., Cont, R., and Smart, G. (2006), Credit Derivatives and
Structured Credit: A Guide for Investors, Chichester, UK: Wiley.

Chaplin, G. (2005), Credit Derivatives: Risk Management, Trading &
Investing, Chichester, UK: Wiley.

Chen, Z. and Glasserman, P. (2008), Fast pricing of basket default
swaps, Operations Research, 56(2), 286--303.

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.

Glasserman, P. (2004), Monte Carlo Methods in Financial Engineering,
volume~53 of Stochastic Modelling and Applied Probability, New York:
Springer Verlag.

Glasserman, P. and Li, J. (2005), Importance sampling for portfolio
credit risk, Management Science, 51(11), 1643--1656.

Gupton, G.M., Finger, C.C., and Bhatia, M. (1997), Credit Metrics
Technical Document, New York: J.P. Morgan & Co.

Hull, J. and White, A. (2004), Valuation of a cdo and an nth to
default cds without 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 the {Li model,
Quantitative Finance, 4, 266--275.

Kalemanova, A., Schmid, B., and Werner, R. (2007), The normal inverse
gaussian distribution for synthetic cdo pricing, The Journal of
Derivatives, 14(3), 80--94.

Laurent, J.P. and Gregory, J. (2005), Basket default swaps, {CDOs and
factor copulas, Journal of Risk, 7(4), 103--122.

Li, D.X. (2000), On default correlation: A copula function approach,
Journal of Fixed Income, 9, 43--54.

Lindskog, F. and RiskLab, ETH (2000), Modelling dependence with
copulas and applications to risk management, Swiss Federal Institute
of Technology Zurich.

Mashal, R. and Zeevi, A. (2002), Beyond correlation: Extreme
co-movements between financial assets, Working paper, Columbia
University.

Schonbucher, P.J. (2003), Credit Derivatives Pricing Models:
Models, Pricing and Implementation, New York: Wiley.

Zheng, H. (2006), Efficient hybrid methods for portfolio credit
derivatives, Quantitative Finance, 6(4), 349--357.
描述 碩士
國立政治大學
統計研究所
97354007
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097354007
資料類型 thesis
dc.contributor.advisor 劉惠美<br>陳麗霞zh_TW
dc.contributor.advisor Liu,Huimei<br>Chen,Li Shyaen_US
dc.contributor.author (Authors) 施明儒zh_TW
dc.contributor.author (Authors) Shih,Ming Juen_US
dc.creator (作者) 施明儒zh_TW
dc.creator (作者) Shih,Ming Juen_US
dc.date (日期) 2009en_US
dc.date.accessioned 5-Sep-2013 15:10:22 (UTC+8)-
dc.date.available 5-Sep-2013 15:10:22 (UTC+8)-
dc.date.issued (上傳時間) 5-Sep-2013 15:10:22 (UTC+8)-
dc.identifier (Other Identifiers) G0097354007en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60430-
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) 97354007zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 蒙地卡羅模擬是在組合信用風險的管理上相當實用的計算工具。衡量組合信用風險時，必須以適當的模型描述資產間的相依性。常態關聯結構是目前最廣為使用的模型，但實證研究認為 t 關聯結構更適合用於配適金融市場的資料。在本文中，我們採用 Bassamboo et al. (2008) 提出的極值相依模型建立 t 關聯結構用以捕捉資產之間的相關性。同時，為增進蒙地卡羅法之收斂速度，我們以 Chiang et al. (2007) 的重要性取樣法為基礎，將其拓展到極值相依模型下，並提出兩階段的重要性取樣技巧確保使用此方法估計一籃子信用違約時，所有模擬路徑均會發生信用事件。數值結果顯示，所提出的演算法皆達變異數縮減。而在模型自由度較低或是資產池較大的情況下，兩階段的重要性取樣法將會有更佳的估計效率。我們也以同樣的思路，提出用以估計投資組合損失機率的演算法。雖然所提出的演算法經過重要性取樣的技巧後仍無法使得欲估計的事件在所有模擬路徑下都會發生，但數值結果仍顯示所提出的方法估計效率遠遠優於傳統蒙地卡羅法。zh_TW
dc.description.abstract (摘要) Monte Carlo simulation is a useful tool on portfolio credit risk management. When measuring portfolio credit risk, one should choose an appropriate model to characterize the dependence among all assets. Normal copula is the most widely used mechanism to capture this dependence structure, however, some emperical studies suggest that $t$-copula provides a better fit to market data than normal copula does. In this article, we use extremal depence model proposed by Bassamboo et al. (2008) to construct $t$-copula. We also extend the importance sampling (IS) procedure proposed by Chiang et al. (2007) to evaluate basket credit default swaps (BDS) with extremal dependence and introduce a two-step IS algorithm which ensures credit events always take place for every simulation path. Numerical results show that the proposed methods achieve variance reduction. If the model has lower degree of freedom, or the portfolio size is larger, the two-step IS method is more efficient. Following the same idea, we also propose algorithms to estimate the probability of portfolio losses. Althought the desired events may not occur for some simulations, even if the IS technique is applied, numerical results still show that the proposed method is much better than crude Monte Carlo.en_US
dc.description.tableofcontents 中文摘要 .......................................... i
英文摘要 .......................................... ii
誌謝 .............................................. iii
目錄 ............................................... iv
表目錄 ............................................. vi
圖目錄 ........................................... viii
第一章 緒論 ........................................ 1
第二章 聯合違約模型 ................................ 5
第三章 一籃子信用違約交換與重要性取樣法 ............ 9
第一節 評價第 $k$ 家標的違約之信用違約交換 ...... 10
第一節 重要性取樣法 ............................. 12
第一節 數值範例 ................................. 18
第四章 極值相依模型下兩階段重要性取樣演算法 ....... 21
第一節 極值相依模型 ............................. 21
第一節 重要性取樣法 ............................. 24
第一節 兩階段重要性取樣法 ....................... 27
第一節 數值結果 ................................. 32
第五章 投資組合損失機率 ........................... 43
第一節 極值相依下之投資組合損失 ................. 43
第一節 條件風險機率與重要性取樣法 ............... 44
第一節 數值結果 ................................. 50
第六章 結論與建議 ................................. 54
參考文獻 ........................................... 55		zh_TW
dc.format.extent 1278824 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097354007en_US
dc.subject (關鍵詞) 蒙地卡羅法zh_TW
dc.subject (關鍵詞) 組合信用風險zh_TW
dc.subject (關鍵詞) t 關聯結構zh_TW
dc.subject (關鍵詞) 極值相依zh_TW
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zh_TW
dc.subject (關鍵詞) 變異數縮減zh_TW
dc.subject (關鍵詞) Monte Carlo methoden_US
dc.subject (關鍵詞) Portfolio credit risken_US
dc.subject (關鍵詞) t-copulaen_US
dc.subject (關鍵詞) Extremal dependenceen_US
dc.subject (關鍵詞) Basket credit default swapsen_US
dc.subject (關鍵詞) Importance samplingen_US
dc.subject (關鍵詞) Variance reductionen_US
dc.title (題名) 評估極值相依組合信用風險之有效演算法zh_TW
dc.title (題名) Efficient Algorithms for Evaluating Portfolio Credit Risk with Extremal Dependenceen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Bassamboo, A., Juneja, S., and Zeevi, A. (2008), Portfolio credit risk
with extremal dependence: Asymptotic analysis and efficient simulation,
Operations Research, 56(3), 593--606.

Bruyere, R., Cont, R., and Smart, G. (2006), Credit Derivatives and
Structured Credit: A Guide for Investors, Chichester, UK: Wiley.

Chaplin, G. (2005), Credit Derivatives: Risk Management, Trading &
Investing, Chichester, UK: Wiley.

Chen, Z. and Glasserman, P. (2008), Fast pricing of basket default
swaps, Operations Research, 56(2), 286--303.

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.

Glasserman, P. (2004), Monte Carlo Methods in Financial Engineering,
volume~53 of Stochastic Modelling and Applied Probability, New York:
Springer Verlag.

Glasserman, P. and Li, J. (2005), Importance sampling for portfolio
credit risk, Management Science, 51(11), 1643--1656.

Gupton, G.M., Finger, C.C., and Bhatia, M. (1997), Credit Metrics
Technical Document, New York: J.P. Morgan & Co.

Hull, J. and White, A. (2004), Valuation of a cdo and an nth to
default cds without 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 the {Li model,
Quantitative Finance, 4, 266--275.

Kalemanova, A., Schmid, B., and Werner, R. (2007), The normal inverse
gaussian distribution for synthetic cdo pricing, The Journal of
Derivatives, 14(3), 80--94.

Laurent, J.P. and Gregory, J. (2005), Basket default swaps, {CDOs and
factor copulas, Journal of Risk, 7(4), 103--122.

Li, D.X. (2000), On default correlation: A copula function approach,
Journal of Fixed Income, 9, 43--54.

Lindskog, F. and RiskLab, ETH (2000), Modelling dependence with
copulas and applications to risk management, Swiss Federal Institute
of Technology Zurich.

Mashal, R. and Zeevi, A. (2002), Beyond correlation: Extreme
co-movements between financial assets, Working paper, Columbia
University.

Schonbucher, P.J. (2003), Credit Derivatives Pricing Models:
Models, Pricing and Implementation, New York: Wiley.

Zheng, H. (2006), Efficient hybrid methods for portfolio credit
derivatives, Quantitative Finance, 6(4), 349--357.		zh_TW