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Intra-Horizon Risk Measures and Management
Yen, Simon H.
Brownian bridge process
|Issue Date: ||2018-06-12 17:16:10 (UTC+8)|
|Abstract: ||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。
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.
|Reference: ||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.
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.
Carr, P., and L. Wu, 2003, “Finite Moment Log Stable Process and Option Pricing,” Journal of Finance 58, 753 – 777.
Daníelsson, J., and J-P Zigrand, 2006, “On Time-Scaling of Risk and the Square-Root- of-Time Rule,” Journal of Banking and Finance, Vol. 30, No. 10, 2701 – 2714.
Dowd, K., 2005, Measuring Market Risk, 2nd ed., John Wiley & Sons Ltd.
Gallati, R. R., 2003, Risk Management and Capital Adequacy, New York: McGraw- Hill.
Gordy, 2003, “A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules,” Journal of Financial Intermediation, 12(3), 199 – 232.
Hanson, S., and T. Schuermann, 2006, “Confidence Intervals for Probabilities of Default,” Journal of Banking and Finance, Vol. 30, No. 8, 2281 – 2301.
Kondor, P., 2009, “Risk in Dynamic Arbitrage: The Price Effects of Convergence Trading,” The Journal of Finance, Vol. 64, No. 2, 631 – 655.
Koopman, S.J., A. Lucas, and P. Klaassen, 2005, “Empirical Credit Cycles and Capital Buffer Formation,” Journal of Banking and Finance, Vol. 29, No. 12, 3159 – 3179.
Kritzman, M. and D. Rich, 2002, “The Mismeasurement of Risk,” Financial Analysts Journal, Vol. 58, No. 3, 91 – 99.
Kupiec, P. H., 1995, “Techniques for Verifying the Accuracy of Risk Measurement Models,” The Journal of Derivatives, Vol. 3, No. 2, 73 – 84.
Liu, J., and F. A. Longstaff, 2004, “Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities,” The Review of Financial Studies, Vol. 17, No. 3, 611 – 641.
Merton, R.C., 1976, “Option Pricing when Underlying Stock Returns Are Discontinuous,” Journal of Financial Economics 3, 125 – 144.
Merton, R., 1974, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance 29, 449 – 470.
Novikov, A., 1971, “On Stopping Times for a Wiener Process,” Theory of Probability and Its Applications, Vol. 16, No. 3, 449 – 456.
Novikov, A., V. Frishling, and N. Kordzakhia, 1999, “Approximations of Boundary Crossing Probabilities for a Brownian Motion,” Journal of Applied Probability, 36, 1019 – 1030.
Overdahl, J. and H. McMillan, 1998, “Another Day, Another Collar: An Evaluation of the Effects of NYSE Rule 80A on Trading Costs and Intermarket Arbitrage,” Journal of Business, 71, 27 – 53.
Pastor, L., and R.F. Stambaugh, 2011, “Are Stocks Really Less Volatile in the Long Run?” (March 22, 2011). EFA 2009 Bergen Meetings Paper; AFA 2010 Atlanta Meetings Paper. Available at SSRN: http://ssrn.com/abstract=1136847.
Reisz, A.S. and C. Perlich, 2007, “A Market-based Framework for Bankruptcy Prediction,” Journal of Financial Stability, Vol. 3, Iss. 2, 85 – 131.
Schuermann, T., 2004, “What Do We Know About Loss-Given-Default?,” in: D. Shimko (Ed.), Credit Risk Models and Management, 2nd ed., 9: 249 – 274, London, UK: Risk Books.
Shleifer, A., and R. Vishny, 1997, “The Limits of Arbitrage,” Journal of Finance, 52, 35 – 55.
Standard & Poor’s RatingsDirect®, 2011, “Default, Transition, and Recovery: 2010 Annual Global Corporate Default Study and Rating Transitions,” Global Credit Portal, March 30, 2011.
Stulz, R.M., 2009, “Six Ways Companies Mismanage Risk,” Harvard Business Review, v87(3), 86 – 94.
Stulz, R.M., 1996, “Rethinking Risk Management,” Journal of Applied Corporate Finance, Vol. 9, No. 3, 8 – 24.
Tarashev N. and H. Zhu, 2008, “Specification and Calibration Errors in Measures of Portfolio Credit Risk: The Case of the ASRF Model,” International Journal of Central Banking, Vol. 4, No. 2, 129 – 173.
Vasicek, O.A., 2002, “Loan Portfolio Value,” Risk Magazine, December 2002, 160 – 162.
Vasicek, O.A., 1987, “Probability of Loss on Loan Portfolio,” KMV Corporation, available at: http://www.moodyskmv.com/research/files/wp/Probability_of_Loss_ on_Loan_Portfolio.pdf.
Wang, C., and T. Wu, 2010, “Futures and Futures Options with Basis Risk: Theoretical and Empirical Perspectives,” Quantitative Finance, Vol. 11, No. 3, 477 – 485.
Wong, H.Y., and T.W. Choi, 2009, “Estimating Default Barriers from Market Information,” Quantitative Finance, Vol. 9, No. 2, 187-196.
Xiong, W., 2001, “Convergence Trading with Wealth Effects: An Amplification Mechanism in Financial Markets,” Journal of Financial Economics, Vol. 62, 247 – 292.
Yi, C., 2010, “On the First Passage Time Distribution of an Ornstein-Uhlenbeck Process,” Quantitative Finance, Vol. 10, No. 9, 957 – 960.
|Source URI: ||http://thesis.lib.nccu.edu.tw/record/#G0091357501|
|Data Type: ||thesis|
|Appears in Collections:||[財務管理學系] 學位論文|
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