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題名 組合型選擇權的評價與其在風險控管的應用
作者 邱政維
貢獻者 廖四郎
邱政維
日期 2002
上傳時間 9-May-2016 16:30:32 (UTC+8)
摘要 　　本文對組合型選擇權（Basket option）在Heath, Jarrow, and Morton（1992）的瞬間遠期利率環境下，提出了三個近似解，分別利用了Vorst（1992）提出的幾何平均近似算術平均的方法，以及Milevsky and Posner（1998）提出的Reciprocal gamma distribution近似多個對數常態（lognormal distribution）算術平均的分配。利用蒙地卡羅模擬法（Monte Carlo Simulation）模擬十萬次的結果發現，本文所提出的近似解，不論在組合型買權或是組合型賣權上都有相當不錯的近似結果。同時，本文也利用了蒙地卡羅模擬法模擬出在到期日時可能的投資組合價值分配，與兩種近似法所求得的分配比較，發現Reciprocal gamma distribution更能捕捉多個對數常態分配算術平均的分配。\r\n　　驗證近似解之後，本文針對組合型選擇權在風險控管上的應用，與其它方法做了比較，這其中包含了：停損策略（Stop-loss）、固定比例策略（Constant-mix）、固定比例投資組合保險（CPPI）、動態複製賣權（Synthetic put）、以及積極風險值管理（active VaR management）。在本文中，我們把這些投資策略視為如同「複製賣權」的動態複製法，其目的在於複製某種金融商品期末的報酬，即可利用選擇權評價理論來求得其期初價值，就可以用此期初價值以及期末報酬型態做比較。
　　This article provides the closed-form approximations for valuing basket option under Gaussian Heath-Jarrow-Morton framework. The approximations we employ to the sum of lognormal random variable are: 1) lognormal distribution and 2) Reciprocal gamma distribution. Based on the numerical results, we find that the two ways have fairly good performances, and the latter has a better approximation to the sum of lognormal distribution.\r\n　　In the second part of this paper, we compare so-called “synthetic put strategy” with other methods in portfolio insurance, including: 1) stop-loss, 2) constant-mix, and 3) constant proportion portfolio insurance, and active VaR management. In order to compare them on a common base, this paper thinks of them in a new point of view that these methods should be viewed as a way to dynamically replicate a derivative, so that we could price those derivatives using Monte Carlo simulation.
參考文獻 1.陳松男及鄭翔伊，1991，”組合型權證的正確評價及避險方法”，證券發展季刊 第十一卷第四期\r\n2.Andre F. Perold, William F. Sharpe, January-February 1988, “Dynamic Strategies for Asset Allocation”, Financial Analysts Journal, pp. 16-27.\r\n3.Bala Arshanapalli, T.Daniel Coggin, William Nelson, Spring 2001, “Is Fixed-Weight Asset Allocation Really Better?”, Journal of Portfolio Management, pp.27-38.\r\n4.Benedicte Alziary, Jean-Pual Decamps, Pierre-Francoies Koehl, 1997, “A P.D.E Approach to Asian Options: Analysis and Numerical Evidence”, Journal of Banking and Finance ,21, pp. 613-640.\r\n5.C. B. Garcia, F. J. Gould, July-August 1987, “Am Empirical Study of Portfolio Insurance.”, Financial Analysts Journal, pp. 44-54.\r\n6.Curran, M., Dec 1994, “Valuing Asian and Portfolio Options by Conditioning on Geometric Mean Price”, Management Science, 40, pp. 1705-1711.\r\n7.Fischer Black, Robert Jones, Fall 1987, “Simplifying portfolio insurance”, Journal of Portfolio Management, pp. 48-51.\r\n8.German, H., El Karoui, N., Rochet, J. C., 1995, “Change of Numeraire, Changes of Probability Measures and Pricing of Options”, Journal of Applied Probability, 32, pp. 313-365.\r\n9.Gentle, D. June 1993, “Basket Weaving”, Risk, 6, pp. 51-52.\r\n10.Heath, D., Jarrow, R., Morton, A., 1992a, “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation”, Econometrica, 60, pp.70-105.\r\n11.Hull, John C., Alan White, 1993, “Efficient Procedures for Valuing European and American Path-Dependent Options”, Journal of Derivatives, 1, pp. 21-31.\r\n12.Huynh, C. B., May 1994, “Back to Baskets”, Risk, 7, pp.55-61.\r\n13.Jose R. Aragones, Carlos Blanco, Juan Mascarenas, Spring 2001, “Active Management of Equity Investment Portfolios”, Journal of Portfolio Management, pp. 39-43.\r\n14.Kemma, A., A. Vorst, 1990, “A Pricing Method for Options Based on Average Asset Values”, Journal of Banking and Financing, 14, pp. 113-129.\r\n15.Mark Rubinstein, July-August 1985, “Alternative Paths to Portfolio Insurance”, Financial Analysts Journal, pp. 42-51.\r\n16.Mark Rubinstein, Hayne E. Leland, July-August 1981, “Replicating Options with Positions in Stock and Cash”, Financial Analysts Journal, pp.63-72.\r\n17.Moshe Arye Milevsky, Steven E. Posner, Summer 1998, “A Closed-Form Approximation for Valuing Basket Options”, Journal of Derivatives, pp. 54-61.\r\n18.Moshe Arye Milevsky, Steven E. Posner, Summer 1999, “Another Moment for the Average Option”, Derivatives Quarterly, pp. 47-53.\r\n19.Philippe Jorion, 2000, “Value at Risk: The New Benchmark for Managing Financial Risk”, second edition, The McGraw-Hill Companies, Inc.\r\n20.Rachel Campbell, Ronald Huisman, Kees Koedijk, 2001, “Optimal Portfolio Selection in a Value-at-Risk Framework”, Journal of Banking & Finance, 25, pp.1789-1804.\r\n21.Richard Bookstaber, Joseph A. Langsam, 2000, “Portfolio Insurance Trading Rules”, Journal of Futures Markets, pp.41-57.\r\n22.Richard M. Ennis, Spring 2001, “The Case for Whole-Stock Portfolios”, Journal of Portfolio Management, pp. 17-26.\r\n23.Roger G. Clarke, Robert D. Arnott, November-December 1987, “The Cost of Portfolio Insurance: Tradeoffs and Choices”, Financial Analysts Journal, pp. 35-47.\r\n24.Szu-Lang Liao, Chou-Wen Wang, 2001, “Monte Carlo Simulation Methods of Option Pricing under Stochastic Interest Rates — with An Application to HJM Model”, Working paper.\r\n25.Vorst, T. March 1992, “Prices and Hedge Ratios of Average Exchange Rate Options”, International Review of Financial Analysis, 1, pp. 179-193.
描述 碩士
國立政治大學
金融研究所
89352009
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2010000305
資料類型 thesis
dc.contributor.advisor 廖四郎zh_TW
dc.contributor.author (Authors) 邱政維zh_TW
dc.creator (作者) 邱政維zh_TW
dc.date (日期) 2002en_US
dc.date.accessioned 9-May-2016 16:30:32 (UTC+8)-
dc.date.available 9-May-2016 16:30:32 (UTC+8)-
dc.date.issued (上傳時間) 9-May-2016 16:30:32 (UTC+8)-
dc.identifier (Other Identifiers) A2010000305en_US
dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=107718-
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) 89352009zh_TW
dc.description.abstract (摘要) 　　本文對組合型選擇權（Basket option）在Heath, Jarrow, and Morton（1992）的瞬間遠期利率環境下，提出了三個近似解，分別利用了Vorst（1992）提出的幾何平均近似算術平均的方法，以及Milevsky and Posner（1998）提出的Reciprocal gamma distribution近似多個對數常態（lognormal distribution）算術平均的分配。利用蒙地卡羅模擬法（Monte Carlo Simulation）模擬十萬次的結果發現，本文所提出的近似解，不論在組合型買權或是組合型賣權上都有相當不錯的近似結果。同時，本文也利用了蒙地卡羅模擬法模擬出在到期日時可能的投資組合價值分配，與兩種近似法所求得的分配比較，發現Reciprocal gamma distribution更能捕捉多個對數常態分配算術平均的分配。\r\n　　驗證近似解之後，本文針對組合型選擇權在風險控管上的應用，與其它方法做了比較，這其中包含了：停損策略（Stop-loss）、固定比例策略（Constant-mix）、固定比例投資組合保險（CPPI）、動態複製賣權（Synthetic put）、以及積極風險值管理（active VaR management）。在本文中，我們把這些投資策略視為如同「複製賣權」的動態複製法，其目的在於複製某種金融商品期末的報酬，即可利用選擇權評價理論來求得其期初價值，就可以用此期初價值以及期末報酬型態做比較。zh_TW
dc.description.abstract (摘要) 　　This article provides the closed-form approximations for valuing basket option under Gaussian Heath-Jarrow-Morton framework. The approximations we employ to the sum of lognormal random variable are: 1) lognormal distribution and 2) Reciprocal gamma distribution. Based on the numerical results, we find that the two ways have fairly good performances, and the latter has a better approximation to the sum of lognormal distribution.\r\n　　In the second part of this paper, we compare so-called “synthetic put strategy” with other methods in portfolio insurance, including: 1) stop-loss, 2) constant-mix, and 3) constant proportion portfolio insurance, and active VaR management. In order to compare them on a common base, this paper thinks of them in a new point of view that these methods should be viewed as a way to dynamically replicate a derivative, so that we could price those derivatives using Monte Carlo simulation.en_US
dc.description.tableofcontents 謝辭\r\n摘要-----I\r\n目錄-----II\r\n表次-----IV\r\n圖次-----V\r\n第一章　緒論-----1\r\n　　第一節　研究動機與目的-----1\r\n　　第二節　研究架構-----2\r\n第二章　相關文獻探討-----3\r\n　　第一節　組合型選擇權部份-----3\r\n　　第二節　投資組合保險部份-----3\r\n第三章　評價模型-----5\r\n　　第一節　環境設定-----5\r\n　　第二節　近似解推導-----7\r\n　　第三節　近似解的比較-----18\r\n　　第四節　近似解的退化型式-----19\r\n第四章　近似解數值分析-----22\r\n　　第一節　數值結果-----22\r\n　　第二節　圖形分析-----24\r\n第五章　風險控管的應用-----27\r\n　　第一節　風險控管的方法-----27\r\n　　第二節　比較方法-----28\r\n　　第三節　數值結果-----29\r\n第六章　結論與建議-----41\r\n　　第一節　研究結論-----41\r\n　　第二節　未來研究建議-----41\r\n參考文獻-----43\r\n\r\n表次\r\n表4-1　模擬投資組合的初始條件與持有數量-----22\r\n表4-2　近似解與模擬值的比較-----23\r\n表4-3　以式子(3.23)的退化型式來評價單─股票選擇權-----26\r\n表5-1　基本資料-----29\r\n表5-2　各種投資策略的比較-----29\r\n\r\n圖次\r\n圖1-1　本文研究架構-----2\r\n圖4-1　投資組合在到期日價格的分配-----24\r\n圖4-2　幾何平均近似結果-----25\r\n圖4-3　Reciprocal gamma distribution近似結果-----25\r\n圖4-4　Reciprocal gamma distribution近似單一對數常態的結果-----26\r\n圖5-1　停損策略的報酬型態-----30\r\n圖5-2　停損策略的報酬分配-----30\r\n圖5-3　固定比例策略的報酬型態-----32\r\n圖5-4　固定比例策略的報酬分配-----32\r\n圖5-5　買進持有與固定比例策略的比較-----33\r\n圖5-6　固定投資組合保險的報酬型態-----34\r\n圖5-7　固定投資組合保險的報酬分配-----34\r\n圖5-8　複製賣權的報酬型態（未加入融資成本）-----36\r\n圖5-9　複製賣權的報酬分配（未加入融資成本）-----36\r\n圖5-10　停損策略與複製賣權的比較-----37\r\n圖5-11　風險值管理的報酬型態-----38\r\n圖5-12　風險值管理的報酬分配-----38\r\n圖5-13　風險值管理的資金分配-----39zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2010000305en_US
dc.title (題名) 組合型選擇權的評價與其在風險控管的應用zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 1.陳松男及鄭翔伊，1991，”組合型權證的正確評價及避險方法”，證券發展季刊 第十一卷第四期\r\n2.Andre F. Perold, William F. Sharpe, January-February 1988, “Dynamic Strategies for Asset Allocation”, Financial Analysts Journal, pp. 16-27.\r\n3.Bala Arshanapalli, T.Daniel Coggin, William Nelson, Spring 2001, “Is Fixed-Weight Asset Allocation Really Better?”, Journal of Portfolio Management, pp.27-38.\r\n4.Benedicte Alziary, Jean-Pual Decamps, Pierre-Francoies Koehl, 1997, “A P.D.E Approach to Asian Options: Analysis and Numerical Evidence”, Journal of Banking and Finance ,21, pp. 613-640.\r\n5.C. B. Garcia, F. J. Gould, July-August 1987, “Am Empirical Study of Portfolio Insurance.”, Financial Analysts Journal, pp. 44-54.\r\n6.Curran, M., Dec 1994, “Valuing Asian and Portfolio Options by Conditioning on Geometric Mean Price”, Management Science, 40, pp. 1705-1711.\r\n7.Fischer Black, Robert Jones, Fall 1987, “Simplifying portfolio insurance”, Journal of Portfolio Management, pp. 48-51.\r\n8.German, H., El Karoui, N., Rochet, J. C., 1995, “Change of Numeraire, Changes of Probability Measures and Pricing of Options”, Journal of Applied Probability, 32, pp. 313-365.\r\n9.Gentle, D. June 1993, “Basket Weaving”, Risk, 6, pp. 51-52.\r\n10.Heath, D., Jarrow, R., Morton, A., 1992a, “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation”, Econometrica, 60, pp.70-105.\r\n11.Hull, John C., Alan White, 1993, “Efficient Procedures for Valuing European and American Path-Dependent Options”, Journal of Derivatives, 1, pp. 21-31.\r\n12.Huynh, C. B., May 1994, “Back to Baskets”, Risk, 7, pp.55-61.\r\n13.Jose R. Aragones, Carlos Blanco, Juan Mascarenas, Spring 2001, “Active Management of Equity Investment Portfolios”, Journal of Portfolio Management, pp. 39-43.\r\n14.Kemma, A., A. Vorst, 1990, “A Pricing Method for Options Based on Average Asset Values”, Journal of Banking and Financing, 14, pp. 113-129.\r\n15.Mark Rubinstein, July-August 1985, “Alternative Paths to Portfolio Insurance”, Financial Analysts Journal, pp. 42-51.\r\n16.Mark Rubinstein, Hayne E. Leland, July-August 1981, “Replicating Options with Positions in Stock and Cash”, Financial Analysts Journal, pp.63-72.\r\n17.Moshe Arye Milevsky, Steven E. Posner, Summer 1998, “A Closed-Form Approximation for Valuing Basket Options”, Journal of Derivatives, pp. 54-61.\r\n18.Moshe Arye Milevsky, Steven E. Posner, Summer 1999, “Another Moment for the Average Option”, Derivatives Quarterly, pp. 47-53.\r\n19.Philippe Jorion, 2000, “Value at Risk: The New Benchmark for Managing Financial Risk”, second edition, The McGraw-Hill Companies, Inc.\r\n20.Rachel Campbell, Ronald Huisman, Kees Koedijk, 2001, “Optimal Portfolio Selection in a Value-at-Risk Framework”, Journal of Banking & Finance, 25, pp.1789-1804.\r\n21.Richard Bookstaber, Joseph A. Langsam, 2000, “Portfolio Insurance Trading Rules”, Journal of Futures Markets, pp.41-57.\r\n22.Richard M. Ennis, Spring 2001, “The Case for Whole-Stock Portfolios”, Journal of Portfolio Management, pp. 17-26.\r\n23.Roger G. Clarke, Robert D. Arnott, November-December 1987, “The Cost of Portfolio Insurance: Tradeoffs and Choices”, Financial Analysts Journal, pp. 35-47.\r\n24.Szu-Lang Liao, Chou-Wen Wang, 2001, “Monte Carlo Simulation Methods of Option Pricing under Stochastic Interest Rates — with An Application to HJM Model”, Working paper.\r\n25.Vorst, T. March 1992, “Prices and Hedge Ratios of Average Exchange Rate Options”, International Review of Financial Analysis, 1, pp. 179-193.zh_TW