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題名 期間內風險衡量與管理
Intra-Horizon Risk Measures and Management
作者 林劭杰
Lin, Shao-Chieh
貢獻者 顏錫銘
Yen, Simon H.
林劭杰
Lin, Shao-Chieh
關鍵詞 期間內風險
風險值
新巴塞爾資本協定
內部評等法資本計提公式
套利部位
布朗橋隨機過程
Intra-Horizon risk
Value-at-Risk
Basel II
IRB approach
Arbitrage positions
Brownian bridge process
日期 2011
上傳時間 12-Jun-2018 17:16:10 (UTC+8)
摘要 傳統的風險衡量指標（例如風險值、期望短缺）通常僅著重在持有期間到期時所可能發生的損失，而忽略了在持有期間到期前的風險。但是，從歷次的金融危機可知，這種做法並不能完全反映投資人在部位持有期間所面臨的所有風險。有鑑於此，本文目的乃在探討期間內風險(Intra-Horizon Risk)的衡量及其在風險管理上的應用。
既有文獻對於期間內風險的討論並不多，因此，我們首先回顧整理既有文獻之研究結果，探討各種期間內風險衡量指標，包括：期間內風險值(Intra-Horizon Value-at-Risk, IHVaR)、期間內期望短缺(Intra-Horizon Expected Shortfall, IHES)，以及期間內超限機率(Intra-Horizon Probability of Breaching, IHPB)。結果發現，最可能為既有風險衡量模型帶來額外貢獻的是期間內超限機率(IHPB)。
其次則進一步將期間內風險的觀念應用在信用風險上，以便納入借款人在債務到期前即提前違約之風險。我們根據所給定的違約機率與違約損失率，推估各信評等級公司暴險的最差情境違約機率(WCPD)，將之與新巴塞爾協定(Basel II)內部評等法資本計提公式(IRB Formula)的結果進行分析比較。結果發現，在考慮期間內風險後，信用品質較佳的暴險反而會受到較大的不利衝擊，且系統性因子的變化路徑會帶來關鍵性的影響：若假設系統性因子以線性方式下滑，則其結果會與內部評等法相近；但如果系統性因子是一直沿著最差情境的路徑走，則所有信評等級暴險的應計提資本都將比內部評等法資本計提公式所算出的高，尤其是投資等級暴險，其應計提資本的增加幅度都在9.5%以上。
最後，我們將期間內風險運用到套利、期貨／現貨避險…等交易策略。這類策略的特色是若能持有至到期，則幾乎無風險；但過往的事件與文獻已指出，其風險仍可能對金融體系造成嚴重的問題。因此，我們推導出在布朗橋隨機過程下的IHVaR一般化近似解，並用以衡量S&P 500指數套利策略之風險。實證結果顯示，在1990年以後，我們的IHVaR一般化近似解表現較歷史模擬法為佳。
Traditional risk measures, such as Value-at-Risk and Expected Shortfall, generally estimated only the possible losses at the end of the holding period, but ignored the risks before the end of the time horizon. However, from the experiences of recent financial crises, we have learned that such risk measures failed to reflect all the risks that investors actually faced during the holding period. In view of this, this dissertation contains three essays to discuss the measurement of intra-horizon risks and their applications in risk management.
In the first essay, we reviewed the existing literature regarding “intra-horizon risks” and examined the contributions of the three intra-horizon risk measures: Intra-Horizon Value-at-Risk (IHVaR), Intra-Horizon Expected Shortfall (IHES), and Intra-Horizon Probability of Breaching (IHPB). From the numerical examples we found that among the three intra-horizon risk measures, the probability of breaching a certain threshold during the time horizon (IHPB), would be the most promising one to bring additional contributions to the existing risk measurement models.
Next, in the second essay we applied the intra-horizon risk into credit risk modeling to take into account the risks of obligors’ early defaults or liquidations. Given the probabilities of default (PD) and losses given default (LGD), we estimated the worst-case probabilities of default (WCPD) for corporate exposures with different credit ratings, and compared our results with the IRB formula set forth in the Basel II. The comparisons showed that when considering the intra-horizon risks, the exposures with better credit ratings would suffer from larger negative impacts, and the evolving path of the systematic risk factor would play critical role. Specifically, when assuming a linear decreasing path for the systematic risk factor, the intra-horizon risk model would have roughly equivalent results to the IRB formula. But, when assuing a worst-at-any-time path, the capital charges would be definitely higher than the IRB formula; especially for the investment grade exposures, the required capital might increase by more than 9.5%.
Finally, in the last essay we tried to implement the intra-horizon risk to the trading strategies that would be almost riskless when invesors could hold the positions to maturity, such as arbitrage or spot/futures hedging strategies. There have been many papers or financial crisis events confirming that these strategies should be risky and might cause serious problems to the financial systems. Therefore, we derived an IHVaR generalized approximation formula based on the generalized Brownian bridge stochastic process, to facilitate measure the maximum losses that investors might suffer during the time horizon under a certain confidence level. Then, using the S&P 500 index arbitrage strategy with a holding period of 3 months to empirically test the results, we found that our IHVaR generalized approximation has performed better than the historical simulation approach since 1990.
參考文獻 Allen S., 2003, Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk, New York: John Wiley & Sons.
Artzner, P., F. Delbaen, J. Eber, and D. Heath, 1999, “Coherent Measures of Risk,“ Mathematical Finance 9 (November), 203 – 228.
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Bakshi, G. and G. Panayotov, 2010, “First-passage Probability, Jump Models, and Intra-Horizon Risk,” Journal of Financial Economics 95, 20 – 40.
Basel Committee on Banking Supervision, 2011a, “Revisions to the Basel II Market Risk Framework – Updated as of 31 December 2010,” February, available at http://www.bis.org/publ/bcbs193.pdf.
Basel Committee on Banking Supervision, 2011b, “Messages from the Academic Literature on Risk Measurement for the Trading Book,” Working Paper No.19, January, available at http://www.bis.org/publ/bcbs_wp19.pdf.
Basel Committee on Banking Supervision, 2010, “Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems,” December, available at http://www.bis.org/publ/bcbs189_dec2010.pdf.
Basel Committee on Banking Supervision, 2006, “International Convergence of Capital Measurement and Capital Standards: A Revised Framework,” available at http://www.bis.org/publ/bcbs128.pdf.
Basel Committee on Banking Supervision, 2005, “Guidance on Paragraph 468 of the Framework Document,” July, available at http://www.bis.org/publ/bcbs115.pdf.
Basel Committee on Banking Supervision, 1996, “Amendment to the Capital Accord to Incorporate Market Risks,” January, available at http://www.bis.org/publ/bcbs24.pdf.
Beghin, L., and E. Orsingher, 1999, “On the Maximum of the Generalized Brownian Bridge,” Lithuanian Mathematical Journal, Vol. 39, No. 2, 157 – 167.
Black, F., and J.C. Cox, 1976, “Valuing Corporate Securities: Some Effects of Bond Indenture Provisions,” Journal of Finance, Vol. 31, No. 2, 351 – 367.
Bonfim, D., 2009, “Credit Risk Drivers: Evaluating the Contribution of Firm Level Information and of Macroeconomic Dynamics,” Journal of Banking and Finance, Vol. 33, No. 2, 281 – 299.
Boudoukh, J., M. Richardson, R. Stanton, and R. Whitelaw, 2004, “MaxVar: Long-Horizon Value-at-Risk in a Mark-to-market Environment,” Journal of Investment Management, Vol. 2, No. 3, 1 – 6.
Brennan, M. J., and E. S. Schwartz, 1990, “Arbitrage in Stock Index Futures,” Journal of Business, Vol. 63, No. 1, S7 – S31.
Brockman, P., and Turtle, H., 2003, “A Barrier Option Framework for Corporate Security Valuation,” Journal of Financial Economics, Vol. 67, No. 3, 511 – 529.
Bruche, M., and C. González-Aguado, 2010, “Recovery Rates, Default Probabilities, and the Credit Cycle,” Journal of Banking and Finance, Vol. 34, No. 4, 754 – 764.
Carr, P., H. Geman, D. Madan, and M. Yor, 2002, “The Fine Structure of Asset Returns: An Empirical Investigation,” Journal of Business 75, 305 – 332.
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描述 博士
國立政治大學
財務管理研究所
91357501
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0091357501
資料類型 thesis
dc.contributor.advisor 顏錫銘zh_TW
dc.contributor.advisor Yen, Simon H.en_US
dc.contributor.author (Authors) 林劭杰zh_TW
dc.contributor.author (Authors) Lin, Shao-Chiehen_US
dc.creator (作者) 林劭杰zh_TW
dc.creator (作者) Lin, Shao-Chiehen_US
dc.date (日期) 2011en_US
dc.date.accessioned 12-Jun-2018 17:16:10 (UTC+8)-
dc.date.available 12-Jun-2018 17:16:10 (UTC+8)-
dc.date.issued (上傳時間) 12-Jun-2018 17:16:10 (UTC+8)-
dc.identifier (Other Identifiers) G0091357501en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/117637-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 財務管理研究所zh_TW
dc.description (描述) 91357501zh_TW
dc.description.abstract (摘要) 傳統的風險衡量指標（例如風險值、期望短缺）通常僅著重在持有期間到期時所可能發生的損失，而忽略了在持有期間到期前的風險。但是，從歷次的金融危機可知，這種做法並不能完全反映投資人在部位持有期間所面臨的所有風險。有鑑於此，本文目的乃在探討期間內風險(Intra-Horizon Risk)的衡量及其在風險管理上的應用。
既有文獻對於期間內風險的討論並不多，因此，我們首先回顧整理既有文獻之研究結果，探討各種期間內風險衡量指標，包括：期間內風險值(Intra-Horizon Value-at-Risk, IHVaR)、期間內期望短缺(Intra-Horizon Expected Shortfall, IHES)，以及期間內超限機率(Intra-Horizon Probability of Breaching, IHPB)。結果發現，最可能為既有風險衡量模型帶來額外貢獻的是期間內超限機率(IHPB)。
其次則進一步將期間內風險的觀念應用在信用風險上，以便納入借款人在債務到期前即提前違約之風險。我們根據所給定的違約機率與違約損失率，推估各信評等級公司暴險的最差情境違約機率(WCPD)，將之與新巴塞爾協定(Basel II)內部評等法資本計提公式(IRB Formula)的結果進行分析比較。結果發現，在考慮期間內風險後，信用品質較佳的暴險反而會受到較大的不利衝擊，且系統性因子的變化路徑會帶來關鍵性的影響：若假設系統性因子以線性方式下滑，則其結果會與內部評等法相近；但如果系統性因子是一直沿著最差情境的路徑走，則所有信評等級暴險的應計提資本都將比內部評等法資本計提公式所算出的高，尤其是投資等級暴險，其應計提資本的增加幅度都在9.5%以上。
最後，我們將期間內風險運用到套利、期貨／現貨避險…等交易策略。這類策略的特色是若能持有至到期，則幾乎無風險；但過往的事件與文獻已指出，其風險仍可能對金融體系造成嚴重的問題。因此，我們推導出在布朗橋隨機過程下的IHVaR一般化近似解，並用以衡量S&P 500指數套利策略之風險。實證結果顯示，在1990年以後，我們的IHVaR一般化近似解表現較歷史模擬法為佳。		zh_TW
dc.description.abstract (摘要) Traditional risk measures, such as Value-at-Risk and Expected Shortfall, generally estimated only the possible losses at the end of the holding period, but ignored the risks before the end of the time horizon. However, from the experiences of recent financial crises, we have learned that such risk measures failed to reflect all the risks that investors actually faced during the holding period. In view of this, this dissertation contains three essays to discuss the measurement of intra-horizon risks and their applications in risk management.
In the first essay, we reviewed the existing literature regarding “intra-horizon risks” and examined the contributions of the three intra-horizon risk measures: Intra-Horizon Value-at-Risk (IHVaR), Intra-Horizon Expected Shortfall (IHES), and Intra-Horizon Probability of Breaching (IHPB). From the numerical examples we found that among the three intra-horizon risk measures, the probability of breaching a certain threshold during the time horizon (IHPB), would be the most promising one to bring additional contributions to the existing risk measurement models.
Next, in the second essay we applied the intra-horizon risk into credit risk modeling to take into account the risks of obligors’ early defaults or liquidations. Given the probabilities of default (PD) and losses given default (LGD), we estimated the worst-case probabilities of default (WCPD) for corporate exposures with different credit ratings, and compared our results with the IRB formula set forth in the Basel II. The comparisons showed that when considering the intra-horizon risks, the exposures with better credit ratings would suffer from larger negative impacts, and the evolving path of the systematic risk factor would play critical role. Specifically, when assuming a linear decreasing path for the systematic risk factor, the intra-horizon risk model would have roughly equivalent results to the IRB formula. But, when assuing a worst-at-any-time path, the capital charges would be definitely higher than the IRB formula; especially for the investment grade exposures, the required capital might increase by more than 9.5%.
Finally, in the last essay we tried to implement the intra-horizon risk to the trading strategies that would be almost riskless when invesors could hold the positions to maturity, such as arbitrage or spot/futures hedging strategies. There have been many papers or financial crisis events confirming that these strategies should be risky and might cause serious problems to the financial systems. Therefore, we derived an IHVaR generalized approximation formula based on the generalized Brownian bridge stochastic process, to facilitate measure the maximum losses that investors might suffer during the time horizon under a certain confidence level. Then, using the S&P 500 index arbitrage strategy with a holding period of 3 months to empirically test the results, we found that our IHVaR generalized approximation has performed better than the historical simulation approach since 1990.		en_US
dc.description.tableofcontents 摘要 II
ABSTRACT IV
TABLE OF CONTENTS VI
LIST OF FIGURES VIII
LIST OF TABLES X
Chapter 1 Introduction 1
1.1 Motivations of this Dissertation 1
1.2 Review of Modern Risk Measures 3
1.3 Purposes of this Dissertation 4
1.4 Contents of this Dissertation 5
Chapter 2 Re-examining the Contributions of Intra-Horizon Risk Measures 7
2.1 Introduction 7
2.2 Literature Review 10
2.2.1 The Need of Intra-Horizon Risk Measures 11
2.2.2 Methodologies of Intra-Horizon Risk Measures 11
2.2.3 Findings in the Related Papers 14
2.3 Contributions of Intra-Horizon Risk Measures under the Brownian Motion 16
2.3.1 The Risk Measures under the Brownian Motion 17
2.3.2 Contributions of IHVaR and IHES 23
2.3.3 Contributions of IHPB 27
2.4 Concluding Remarks 30
Chapter 3 Applying Intra-Horizon Risk Measures in Banks’ Credit Risk Capital Requirements 32
3.1 Introduction 32
3.2 The IRB Formula 36
3.2.1 Derivation of the IRB Formula 36
3.2.2 Extension to Multiple Years 39
3.2.3 Estimating Probability of Default 41
3.3 The Intra-Horizon Conditional PD 44
3.3.1 Model Setting 44
3.3.2 Estimating Worst-Case Probabilities of Default 46
3.3.3 Estimating Unconditional PD 48
3.4 The Comparisons 49
3.4.1 Comparisons of IRB Formula and Intra-Horizon Case 1 50
3.4.2 Comparisons of IRB formula and Both Intra-Horizon Models 52
3.4.3 Confidence Intervals of WCPDs 55
3.5 Concluding Remarks 57
Chapter 4 The Intra-Horizon Risk Measures of the Arbitrage Positions 59
4.1 Introduction 59
4.2 The Parametric Model Estimating Arbitrage Positions’ IHVaRs 63
4.2.1 The Stochastic Processes of the Arbitrage Portfolio Values 63
4.2.2 Deriving the Solutions to the Intra-Horizon Risk Measures 66
4.3 Applications to the S&P 500 Index Arbitrage 71
4.3.1 The S&P 500 Index Spot-Futures Arbitrage Strategy 71
4.3.2 The Historical Simulation Approach to Estimating IHVaRs 74
4.3.3 The IHVaRs Estimated by Parametric Approach 76
4.3.4 The Backtesting Results 81
4.4 Summary and Conclusions 85
Chapter 5 Conclusions and Further Research 87
5.1 Concluding Remarks 87
5.2 Potential for Further Research 88
References 90		zh_TW
dc.format.extent 2522717 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0091357501en_US
dc.subject (關鍵詞) 期間內風險zh_TW
dc.subject (關鍵詞) 風險值zh_TW
dc.subject (關鍵詞) 新巴塞爾資本協定zh_TW
dc.subject (關鍵詞) 內部評等法資本計提公式zh_TW
dc.subject (關鍵詞) 套利部位zh_TW
dc.subject (關鍵詞) 布朗橋隨機過程zh_TW
dc.subject (關鍵詞) Intra-Horizon risken_US
dc.subject (關鍵詞) Value-at-Risken_US
dc.subject (關鍵詞) Basel IIen_US
dc.subject (關鍵詞) IRB approachen_US
dc.subject (關鍵詞) Arbitrage positionsen_US
dc.subject (關鍵詞) Brownian bridge processen_US
dc.title (題名) 期間內風險衡量與管理zh_TW
dc.title (題名) Intra-Horizon Risk Measures and Managementen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Allen S., 2003, Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk, New York: John Wiley & Sons.
Artzner, P., F. Delbaen, J. Eber, and D. Heath, 1999, “Coherent Measures of Risk,“ Mathematical Finance 9 (November), 203 – 228.
Artzner, P., F. Delbaen, J. Eber, and D. Heath, 1997, “Thinking Coherently,“ Risk 10 (November), 68 – 71.
Bakshi, G. and G. Panayotov, 2010, “First-passage Probability, Jump Models, and Intra-Horizon Risk,” Journal of Financial Economics 95, 20 – 40.
Basel Committee on Banking Supervision, 2011a, “Revisions to the Basel II Market Risk Framework – Updated as of 31 December 2010,” February, available at http://www.bis.org/publ/bcbs193.pdf.
Basel Committee on Banking Supervision, 2011b, “Messages from the Academic Literature on Risk Measurement for the Trading Book,” Working Paper No.19, January, available at http://www.bis.org/publ/bcbs_wp19.pdf.
Basel Committee on Banking Supervision, 2010, “Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems,” December, available at http://www.bis.org/publ/bcbs189_dec2010.pdf.
Basel Committee on Banking Supervision, 2006, “International Convergence of Capital Measurement and Capital Standards: A Revised Framework,” available at http://www.bis.org/publ/bcbs128.pdf.
Basel Committee on Banking Supervision, 2005, “Guidance on Paragraph 468 of the Framework Document,” July, available at http://www.bis.org/publ/bcbs115.pdf.
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