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Title: | 一籃子信用違約交換評價之有效演算法 Efficient algorithms for basket default swap valuation |
Authors: | 李昭儀 |
Contributors: | 劉惠美 陳麗霞 李昭儀 |
Keywords: | 一籃子信用違約交換 變異數縮減 偏斜常態分配 |
Date: | 2009 |
Issue Date: | 2010-12-08 01:53:54 (UTC+8) |
Abstract: | 本研究探討評價一籃子信用商品有效率的估計方法,所謂有效率是指計算簡單、快速且能達到變異數縮減,Chiang, Yueh, and Hsieh (2007)提出一個有效演算法,模型中將系統性風險因子與非系統性風險因子視為常態分配,但考慮現實情況系統性風險因子未必為對稱分配,因此本文系統性風險採用偏斜常態分配,而非系統性風險為常態分配。根據Chiang, Yueh, and Hsieh (2007)所提之演算法,並將其延伸至多個系統性風險因子,探討此方法在系統風險為偏斜常態分配下變異數縮減的效果。以不同的投資組合計算其違約給付金額,並與蒙地卡羅法模擬結果比較,由於此方法皆在至少有k個違約發生的事件下抽樣,因此所需模擬次數較少,計算時間也較短,且可達到變異數縮減。
單一系統性風險因子模型,當 ρ 值高,變異數縮減效果越好,且變異數縮減的效果也隨著 k 值越大效果越好。在二個系統性風險因子模型,變異數縮減的效果也是隨著 k 值越大效果越好。就各因子的權重而言,變異數縮減的效果原則上對權重較大的因子做重點抽樣,變異數縮減效果較顯著,但是此方法對於極為右偏的分配時,對權重較大的因子做重點抽樣效果不彰,此時反而針對對稱分配做重點抽樣的效果較佳。此方法就到期時間做探討,發現到期時間越長變異數縮減效果越差。 |
Reference: | 1. Anderson, Eric C. (1999). “Monte Carlo Methods and Importance Sampling.” Lecture Notes for Stat 578C, Statistical Genetics. 2. Chiang, M.H., Yueh, M.L. and Hsieh, M.H. (2007). “An Efficient Algorithm for Basket Default Swap Valuation.” Journal of Derivatives, pp. 8-19. 3. Chen, Zhiyong and Paul Glasserman (2008). “Fast Pricing of Basket Default Swaps.” Operations Research, Vol. 56, No. 2, pp. 286-303. 4. Gupta, Arjun K., Nguyen, Truc T. and Sanqui, Jose Almer T. (2004). “Characterization of the Skew-normal Distribution.” Annals of the Institute of Statistical Mathematics, pp. 351-360. 5. Glasserman, Paul and Jingyi Li (2005). “Importance Sampling for Portfolio Credit Risk.” Management Science, Vol. 51, pp. 1643-1656. 6. Hull, J. and A. White (2001). “Valuing Credit Default Swap II: Modeling Default Correlation.” Journal of Derivatives, Vol. 3, pp. 12-22. 7. Hull, J. and A. White (2004). “Valuation of a CDO and an nth to Default CDS without Monte Carlo Simulation.” Journal of Derivatives, Vol. 2, pp. 8-23. 8. Laurent, J. P. and J. Gregory (2005). “Basket Default Swaps, CDO’s and Factor Copulas.” Journal of Risk, Vol. 7, No. 4, pp. 103-122. 9. Li, D.X. (2000). “On Default Correlation:A Copula Approach.” Journal of Fixed Income, Vol. 4, pp. 43-54. |
Description: | 碩士 國立政治大學 統計研究所 97354018 98 |
Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0097354018 |
Data Type: | thesis |
Appears in Collections: | [統計學系] 學位論文
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