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題名 跳躍擴散模型下固定比例債務債券評價,風險構面及避險分析
The Pricing, Credit Risk Decomposition and Hedging Analysis of CPDO Under The Jump Diffusion Model
作者 王聖元
Wang , Sheng Yuan
貢獻者 江彌修
Chiang, Mi Hsiu
王聖元
Wang , Sheng Yuan
關鍵詞 信用衍生性商品
固定比例債務債券
跳躍擴散模型
信用風險
蒙地卡羅模擬法
credit derivatives
Constant Proportion Debt Obligations
Jump Diffusion Process
credit risk
Monte Carlo Simulation
日期 2010
上傳時間 29-Sep-2011 16:50:38 (UTC+8)
摘要 信用衍生性商品在市場上交易漸趨熱絡,創新速度更是一日千里,市場上琳琅滿目的信用衍生性商品,投資人要如何審慎客觀評估風險後再檢視自身能承擔的風險後投資,諸如此類的議題在近幾年備受關注。尤其在2007金融海嘯之後,所有信用衍生性產品也無一倖免,信用評等公司對信用衍生性產品的評價,也備受挑戰,因此,辨識風險以及驅避風險在後金融海嘯時期,已是一刻不容緩之待解決問題。固定比例債務債券(Constant Proportion Debt Obligations; CPDO)亦是金融海嘯前一年所發明的創新信用衍生性商品,由於其高收益特性以及強調極低投資風險,吸引了許多投資人爭相購買,但金融海嘯時期,也是付之一炬。為了使投資人更了解此商品的風險,本研究運用在跳躍擴散模型假設下,存在封閉解的雙出場障礙式選擇權複製此商品的風險因子,並且為了描述此商品具有動態調整槓桿的時間相依(Time Dependent)性質,加入了蒙地卡羅模擬法,捕捉任意時點上,投資人面臨的風險,將風險因子拆解選擇權後,也更能讓投資人能以投資選擇權的知識運用到此商品來操作。最後,為了使投資人趨避諸如金融海嘯時期的風險,本研究也用選擇權的Delta 避險策略,替商品虛擬一現貨市場,並模擬出其避險之績效。
The increasing trading volumes and innovative structures of credit derivatives have attracted great academic attention in the quantification and analysis of their complex risk characteristics. The pricing and hedging issues of complex credit structuers after the 2009 financial crisis are especially vital, and they present great challegens to both the academic community and industry practitioners. Constant Proportion Debt Obligations (CPDOs) are one of the new credit-innovations that claim to provide risk-adverse investors with fixed-income cash flows and minimal risk-bearing, yet the cash-outs events of such products during the crisis unfolded risk characteristics that had been unseen to investors. This research focuses on the pricing risk quantification, and dynamic hedging issues of CPDOs under a Levy jump diffusion setting. Based on decomposing the product`s risk structure, we derive explicit closed-form solutions in the form of time-dependent double digital knock-out barrier options. This enables us to explore, in terms of the associated hedging greeks, the embeded risk characteristics of CPDOs and propose feasible delta-netral strategies that are feasible to hedge such products. Numerical simulations are subsequently performed to provide benchmark measures for the proposed hedging strategies.
參考文獻 Baydar, E., Di-Graziano, G. and Korn, R., 2009, “Theoretical solution versus industry standard: Optimal leverage function for CPDOs”, Bl¨atter DGVFM , 30: 15–29.
Carr, P. and Chou, A., 2002, “Hedging complex barrier options”, Working Paper,
Morgan Stanley and MIT Computer Science
Collin-Dufresne, P., Goldstein, R. and Martin, J., 2001, “The Determinants of Credit Spread Changes”, Journal of Finance, Vol. 56, No. 6, 2177-2207.
Collin-Dufresne, P., Goldstein, R. and Helwege, J., 2010, “Is Credit Event Risk Priced? Modeling Contagion via The Updating of Beliefs”, NBER Working Paper Series, 1-48.
Cont, R. and Jessen, C., 2008, “Constant Proportion Debt Obligations(CPDOs)”, Journal of Financial Risks International Forum, March 27-28.
Cont, R. and Tankov, P., 2009, “Constant Proportion Portfolio Insurance in presence of Jumps in Asset Prices”, Mathematical Finance, Vol. 19, Issue 3, 379-401.
Das, S. R., Duffie, D., Kapadia, N. and Saita, L., 2007, “Common Failings: How Corporate Defaults are Correlated”, Journal of Finance, 62(1), 93-117.
Dorn, J., 2010, “Modeling of CPDOs – Identifying optimal and implied leverage”, Journal of Banking & Finance, 34, 1371-1382.
Duffie, D. and Lando, D., 2001, “Term Structures of Credit Spreads with Incomplete Accounting Information”, Econometrica, Vol. 69, Issue 3, 633-664.
Duffie, D., Eckner, A., Horel, G. and Saita, L., 2009, “Frailty Correlated Default”,
Journal of Finance , 64, 2087–2122.
Hull, J. and White, A., 2001, “Valuing Credit Default Swaps II:Modeling Default Correlations,” Journal of Derivatives, 8, No.3, 12-22.
Jarrow, R. and Yu, F., 2001, “Counterparty Risk and the Pricing of Defaultable Securities”, Journal of Finance, vol. LVI, NO.5, 1765-1799.
Jorion, P. and Zhang, G., 2007, “Good and Bad Credit Contagion: Evidence
from Credit Default Swaps”, Journal of Financial Economics, Vol. 84, 860-833.
Jorion, P. and Zhang, G. 2009, “Credit Contagion from Counterparty Risk”, Journal of Finance Volume 64: Issue 5, 2053-2087.
Jossens, E. and Schoutens, W., 2007, “An Overview of Portfolio Insurances:
CPPI and CPDO”, JRC Scientific and Technical Reports , 1-34.
Kou, S. G., 2002, “A Jump Diffusion Model for Option Pricing”, Columbia University working paper
Torresetti, R. and Pallavicini, A., 2009, “Stressing Rating Criteria Allowing for Default Clustering”, Credit Derivatives Structuring-Global Markets-BBVA, 1-51.
Dominion Bond Rating Service, 2007, “CPDOs Laid Bare: Structure, Risk and Rating Sensitivity”, 1-40
描述 碩士
國立政治大學
金融研究所
98352023
99
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098352023
資料類型 thesis
dc.contributor.advisor 江彌修zh_TW
dc.contributor.advisor Chiang, Mi Hsiuen_US
dc.contributor.author (Authors) 王聖元zh_TW
dc.contributor.author (Authors) Wang , Sheng Yuanen_US
dc.creator (作者) 王聖元zh_TW
dc.creator (作者) Wang , Sheng Yuanen_US
dc.date (日期) 2010en_US
dc.date.accessioned 29-Sep-2011 16:50:38 (UTC+8)-
dc.date.available 29-Sep-2011 16:50:38 (UTC+8)-
dc.date.issued (上傳時間) 29-Sep-2011 16:50:38 (UTC+8)-
dc.identifier (Other Identifiers) G0098352023en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/50851-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融研究所zh_TW
dc.description (描述) 98352023zh_TW
dc.description (描述) 99zh_TW
dc.description.abstract (摘要) 信用衍生性商品在市場上交易漸趨熱絡,創新速度更是一日千里,市場上琳琅滿目的信用衍生性商品,投資人要如何審慎客觀評估風險後再檢視自身能承擔的風險後投資,諸如此類的議題在近幾年備受關注。尤其在2007金融海嘯之後,所有信用衍生性產品也無一倖免,信用評等公司對信用衍生性產品的評價,也備受挑戰,因此,辨識風險以及驅避風險在後金融海嘯時期,已是一刻不容緩之待解決問題。固定比例債務債券(Constant Proportion Debt Obligations; CPDO)亦是金融海嘯前一年所發明的創新信用衍生性商品,由於其高收益特性以及強調極低投資風險,吸引了許多投資人爭相購買,但金融海嘯時期,也是付之一炬。為了使投資人更了解此商品的風險,本研究運用在跳躍擴散模型假設下,存在封閉解的雙出場障礙式選擇權複製此商品的風險因子,並且為了描述此商品具有動態調整槓桿的時間相依(Time Dependent)性質,加入了蒙地卡羅模擬法,捕捉任意時點上,投資人面臨的風險,將風險因子拆解選擇權後,也更能讓投資人能以投資選擇權的知識運用到此商品來操作。最後,為了使投資人趨避諸如金融海嘯時期的風險,本研究也用選擇權的Delta 避險策略,替商品虛擬一現貨市場,並模擬出其避險之績效。zh_TW
dc.description.abstract (摘要) The increasing trading volumes and innovative structures of credit derivatives have attracted great academic attention in the quantification and analysis of their complex risk characteristics. The pricing and hedging issues of complex credit structuers after the 2009 financial crisis are especially vital, and they present great challegens to both the academic community and industry practitioners. Constant Proportion Debt Obligations (CPDOs) are one of the new credit-innovations that claim to provide risk-adverse investors with fixed-income cash flows and minimal risk-bearing, yet the cash-outs events of such products during the crisis unfolded risk characteristics that had been unseen to investors. This research focuses on the pricing risk quantification, and dynamic hedging issues of CPDOs under a Levy jump diffusion setting. Based on decomposing the product`s risk structure, we derive explicit closed-form solutions in the form of time-dependent double digital knock-out barrier options. This enables us to explore, in terms of the associated hedging greeks, the embeded risk characteristics of CPDOs and propose feasible delta-netral strategies that are feasible to hedge such products. Numerical simulations are subsequently performed to provide benchmark measures for the proposed hedging strategies.en_US
dc.description.tableofcontents 第壹章 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
第一節 研究動機與目的…………………………………………1
第二節 研究架構 …..…………………………………………….3
第貳章 信用風險文獻探討. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
第參章 基本假設與模型設定 . . . . . . . . . . . . . . . . . . . . . . . . . . .10
第一節 固定比例債務債券評價模型 ………………………...10
第二節 固定比例債務債券的風險衡量指標 ………………….15
第三節 固定比例債務債券避險模型 ...………………………..16
第肆章 數值結果與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
第一節 固定比例債務債券評價分析….….……………………18
第二節 固定比例債務債券風險分析…………………………..21
第三節 固定比例債務債券避險分析…………………………..34
第伍章 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
第一節 結論 ..…………………………………………………...37
第二節 未來研究建議…………………………………………..38
參考文獻 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
附錄一 期望損失之拆解推導過程. . . . . . . . . . . . . . . . . . . . . . . .42
附錄二 風險因子推導過程. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
III
圖目錄
圖1.1 研究架構圖……………………………………………………………………3
圖4.1固定比例債務擔保憑證現金流………………………………………………19
圖4.2情境一資產淨值路徑…………………………………………………………20
圖4.3情境二資產淨值路徑………………………………………………………....20
圖4.4情境三資產淨值路徑…………………………………………………………21
圖4.5情境一資產負債缺口路徑……………………………………………………23
圖4.6情境一之選擇權價值…………………………………………………………23
圖4.7情境一選擇權之delta因子…………………………………………………..24
圖4.8情境一選擇權之vega因子…………………………………………………..25
圖4.9情境一選擇權之theta因子…………………………………………………..25
圖4.10情境二資產負債缺口路徑………………………………………………….26
圖4.11情境二之選擇權價值……………………………………………………….26
圖4.12情境二選擇權之delta因子…………………………………………………27
圖4.13情境二選擇權之vega因子…………………………………………………28
圖4.14情境二選擇權之theta因子…………………………………………………28
圖4.15情境三資產負債缺口路徑………………………………………………….28
圖4.16情境三之選擇權價值……………………………………………………….29
圖4.17情境三選擇權之delta因子………………………………………………...29
圖4.18情境三選擇權之vega因子…………………………………………………30
圖4.19情境三選擇權之theta因子………………………………………………....30
IV
表目錄
表4.1不同情境下的增額等候時間…………………………………………………31
表4.2不同情境下的達成負債目標比率……………………………………………32
表4.3不同情境下的平均資產淨損失率……………………………………………33
表4.4不同情境下每週動態避險後的增額等候時間………………………………34
表4.5不同情境下每週動態避險後的達成負債目標比率…………………………34
表4.6不同情境下每週動態避險後的平均資產淨損失率…………………………35
表4.7不同情境下每半年動態避險後的增額等候時間……………………………35
表4.8 不同情境下每半年動態避險後的達成負債目標比率……………………..36
表4.9不同情境下每半年動態避險後的平均資產淨損失率………………………36
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0098352023en_US
dc.subject (關鍵詞) 信用衍生性商品zh_TW
dc.subject (關鍵詞) 固定比例債務債券zh_TW
dc.subject (關鍵詞) 跳躍擴散模型zh_TW
dc.subject (關鍵詞) 信用風險zh_TW
dc.subject (關鍵詞) 蒙地卡羅模擬法zh_TW
dc.subject (關鍵詞) credit derivativesen_US
dc.subject (關鍵詞) Constant Proportion Debt Obligationsen_US
dc.subject (關鍵詞) Jump Diffusion Processen_US
dc.subject (關鍵詞) credit risken_US
dc.subject (關鍵詞) Monte Carlo Simulationen_US
dc.title (題名) 跳躍擴散模型下固定比例債務債券評價,風險構面及避險分析zh_TW
dc.title (題名) The Pricing, Credit Risk Decomposition and Hedging Analysis of CPDO Under The Jump Diffusion Modelen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Baydar, E., Di-Graziano, G. and Korn, R., 2009, “Theoretical solution versus industry standard: Optimal leverage function for CPDOs”, Bl¨atter DGVFM , 30: 15–29.zh_TW
dc.relation.reference (參考文獻) Carr, P. and Chou, A., 2002, “Hedging complex barrier options”, Working Paper,zh_TW
dc.relation.reference (參考文獻) Morgan Stanley and MIT Computer Sciencezh_TW
dc.relation.reference (參考文獻) Collin-Dufresne, P., Goldstein, R. and Martin, J., 2001, “The Determinants of Credit Spread Changes”, Journal of Finance, Vol. 56, No. 6, 2177-2207.zh_TW
dc.relation.reference (參考文獻) Collin-Dufresne, P., Goldstein, R. and Helwege, J., 2010, “Is Credit Event Risk Priced? Modeling Contagion via The Updating of Beliefs”, NBER Working Paper Series, 1-48.zh_TW
dc.relation.reference (參考文獻) Cont, R. and Jessen, C., 2008, “Constant Proportion Debt Obligations(CPDOs)”, Journal of Financial Risks International Forum, March 27-28.zh_TW
dc.relation.reference (參考文獻) Cont, R. and Tankov, P., 2009, “Constant Proportion Portfolio Insurance in presence of Jumps in Asset Prices”, Mathematical Finance, Vol. 19, Issue 3, 379-401.zh_TW
dc.relation.reference (參考文獻) Das, S. R., Duffie, D., Kapadia, N. and Saita, L., 2007, “Common Failings: How Corporate Defaults are Correlated”, Journal of Finance, 62(1), 93-117.zh_TW
dc.relation.reference (參考文獻) Dorn, J., 2010, “Modeling of CPDOs – Identifying optimal and implied leverage”, Journal of Banking & Finance, 34, 1371-1382.zh_TW
dc.relation.reference (參考文獻) Duffie, D. and Lando, D., 2001, “Term Structures of Credit Spreads with Incomplete Accounting Information”, Econometrica, Vol. 69, Issue 3, 633-664.zh_TW
dc.relation.reference (參考文獻) Duffie, D., Eckner, A., Horel, G. and Saita, L., 2009, “Frailty Correlated Default”,zh_TW
dc.relation.reference (參考文獻) Journal of Finance , 64, 2087–2122.zh_TW
dc.relation.reference (參考文獻) Hull, J. and White, A., 2001, “Valuing Credit Default Swaps II:Modeling Default Correlations,” Journal of Derivatives, 8, No.3, 12-22.zh_TW
dc.relation.reference (參考文獻) Jarrow, R. and Yu, F., 2001, “Counterparty Risk and the Pricing of Defaultable Securities”, Journal of Finance, vol. LVI, NO.5, 1765-1799.zh_TW
dc.relation.reference (參考文獻) Jorion, P. and Zhang, G., 2007, “Good and Bad Credit Contagion: Evidencezh_TW
dc.relation.reference (參考文獻) from Credit Default Swaps”, Journal of Financial Economics, Vol. 84, 860-833.zh_TW
dc.relation.reference (參考文獻) Jorion, P. and Zhang, G. 2009, “Credit Contagion from Counterparty Risk”, Journal of Finance Volume 64: Issue 5, 2053-2087.zh_TW
dc.relation.reference (參考文獻) Jossens, E. and Schoutens, W., 2007, “An Overview of Portfolio Insurances:zh_TW
dc.relation.reference (參考文獻) CPPI and CPDO”, JRC Scientific and Technical Reports , 1-34.zh_TW
dc.relation.reference (參考文獻) Kou, S. G., 2002, “A Jump Diffusion Model for Option Pricing”, Columbia University working paperzh_TW
dc.relation.reference (參考文獻) Torresetti, R. and Pallavicini, A., 2009, “Stressing Rating Criteria Allowing for Default Clustering”, Credit Derivatives Structuring-Global Markets-BBVA, 1-51.zh_TW
dc.relation.reference (參考文獻) Dominion Bond Rating Service, 2007, “CPDOs Laid Bare: Structure, Risk and Rating Sensitivity”, 1-40zh_TW