學術產出-Theses

題名 具有違約風險證券之最適投資組合策略
Optimal Portfolios with Default Risks ─ A Firm Value Approach
作者 陳震寰
Chen, Jen-Huan
貢獻者 張士傑
Chang, Shih-Chieh
陳震寰
Chen, Jen-Huan
關鍵詞 最適投資組合
信用風險
違約風險
彈性
存續期間
Optimal portfolios
credit risk
default risk
elasticity
duration
日期 2005
上傳時間 2009-09-18
摘要 關於Merton (1969) 最適投資組合策略問題,所考慮之投資情境為:一個將其財富資金安排配置於風險性資產(各類證券)與無風險短期現金部位之投資人,在給定此投資人心目中財富效用函數之前提下,希望事先決定出投資組合之最適投資權重(策略),藉此達成在投資期滿時極大化財富效用之期望值。基於Merton (1974) 公司價值觀點,具有違約風險之證券(公司債與股票)乃是公司價值之衍生性商品,無法以傳統資產配置對股票與債券部位採取現貨方式處理最適投資策略,在此必需同時結合財務工程處理衍生性金融商品計價與避險之技術來解決。本研究利用Kron & Kraft (2003) 彈性求解法來針對市場是否有投資限制、債券提前違約、到期違約及利率隨機與否等假設,基於不同投資組合情境分析來最適投資部位策略。本研貢獻和究創新突破之處在於特別探討公司違約時,債券投資人不再享有全部公司殘值之求償權,此時股東亦享有部份比例之求償權,違約後之公司殘值將由債券投資人與股東兩者比例共分之特殊情境下,對數型態財富效用之投資人對於提前違約風險之接受度高於到期違約風險,若一般情境(股東無任何求償權)則為相反。此外亦特別提供最適成長投資組合之動態避險策略封閉解,藉以提供投資人面臨企業違約風險時應制定之投資決策與動態調整,使本研究臻至週延與實用。
Under the Merton (1969) optimal portfolio problem, we only consider the specific investor, whose wealth utility follows the type of logarithm function; wants to maximize the expected value of the terminal wealth utility through determine the optimal investment strategy in advance. He divides his wealth into the riskless asset and risky assets such as the money market account and the various-risky securities issued by the corporate.

Based on the Merton firm value framework (1974), the defaultable securities, such as the corporate bonds and stocks, are the derivatives instruments of the firm value. It will be inappropriate if we deal with this optimal portfolio problem under the original methods. Therefore, we need to handle this optimal asset allocation problem through the pricing, valuation and hedging techniques from the financial engineering simultaneously.

This study apply the elasticity approach to portfolio optimization (EAPO, Kraft ,2003) to solve the optimal portfolio strategy under various scenarios, such as the market contains the investment constrain or not, intermediate default risks, mature default risk, interest rate risky under the stochastic process.

The innovation and contribution of this paper are especially breaking the common setting and analysis the optimal-growth-portfolio strategy under the special scenario. In the common setting, as soon as the default event occurs, the residual firm value will be claimed by the corporate bondholders with fully proportion and the stockholder cannot share any residual value. Oppositely, the stockholder will be able to share the residual firm value proportionally with the corporate bondholder together under the so-called special scenario. We found that the investor would have higher acceptance of the premature default risk than the mature default risk in the special scenario. This phenomenon will be reversed under the common scenario.

Furthermore, in order to make this study more completely and useful, we do not only illustrate the optimal investment strategy but also provide the closed-formed solution of the dynamic hedge strategy of the risky position, composed by the defaultable securities. This could help the optimal-growth-portfolio-oriented investor to make investment decision while they face the firm value downward decreasing.
參考文獻 ________________________________________
[01] Black, F., and J. C. Cox, 1976, Valuing corporate securities: Some effects of bond indenture provisions, Journal of Finance 31: 351-367.
[02] Black, F.; and M. Scholes, 1973, The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81: 637-654.
[03] Briys, E., and F. de Varenne, 1997, Valuing risky fixed rate debt: An extension, Journal of Financial and Quantitative Analysis 32: 239-248.
[04] Geske, R., 1977, The valuation of corporate liabilities as compound options, Journal of Financial and Quantitative Analysis 12: 541-552.
[05] Hull, J. C., and A. White, 1995, The impact of default risk on the prices of options and other derivative securities, Journal of Banking and Finance 19: 299-322.
[06] Johnson, H., and R. Stulz, 1987, The pricing of options with default risk, Journal of Finance 42: 267-280.
[07] Karatzas, I., J. P. Lehoczky., and S. E. Shreve, 1987, Optimal portfolio and consumption decisions for a small investor on a finite horizon, SIAM Journal on Control and Optimization 27: 1157-1186.
[08] Kraft, H., 2003, The elasticity approach to portfolio optimization, Mathematical Methods of Operations Research (ZOR) 58: 159–182.
[09] Korn, R., and H. Kraft, 2003, Optimal Portfolios with Defaultable Securities: A Firm Value Approach, International Journal of Theoretical and Applied Finance 6: 793-819.
[10] Longstaff., and Schwartz, 1995, A simple approach to valuing risky fixed and floating rate debt, Journal of Finance 50: 789-819.
[11] Merton, R. C., 1969, Lifetime portfolio selection under uncertainty: the continuous case, Reviews of Economical Statistics 51: 247-257.
[12] Merton, R. C., 1971, Optimal consumption and portfolio rules in a continuous-time model, Journal of Economic Theory 3: 373-413.
[13] Merton, R. C., 1974, On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance 29: 449-479.
[14] Saa-Requejo, J., and Santa-Clara, P, 1999, Bond pricing with default risk, Working paper, UCLA.
[15] Vasicek, O, 1977, An equilibrium characterization of the term structure, Journal of Financial Economics 5: 177-188.
[16] Harrison, J. M., and D. M. Kreps, 1979, Martingales and arbitrage in multi-period securities markets, Journal of Economic Theory 20: 381-408.
[17] Harrison, J. M., and S. R. Pliska, 1981, Martingales and Stochastic Integrals in the theory of Continuous Trading, Stochastic Process. Appl. 11: 215-260.
[18] Ito, K., 1944, Stochastic integral. Proc. Imp. Acad. Tokyo, 20: 519-524.
描述 碩士
國立政治大學
風險管理與保險研究所
93358010
94
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0933580101
資料類型 thesis
dc.contributor.advisor 張士傑zh_TW
dc.contributor.advisor Chang, Shih-Chiehen_US
dc.contributor.author (Authors) 陳震寰zh_TW
dc.contributor.author (Authors) Chen, Jen-Huanen_US
dc.creator (作者) 陳震寰zh_TW
dc.creator (作者) Chen, Jen-Huanen_US
dc.date (日期) 2005en_US
dc.date.accessioned 2009-09-18-
dc.date.available 2009-09-18-
dc.date.issued (上傳時間) 2009-09-18-
dc.identifier (Other Identifiers) G0933580101en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/34175-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 93358010zh_TW
dc.description (描述) 94zh_TW
dc.description.abstract (摘要) 關於Merton (1969) 最適投資組合策略問題,所考慮之投資情境為:一個將其財富資金安排配置於風險性資產(各類證券)與無風險短期現金部位之投資人,在給定此投資人心目中財富效用函數之前提下,希望事先決定出投資組合之最適投資權重(策略),藉此達成在投資期滿時極大化財富效用之期望值。基於Merton (1974) 公司價值觀點,具有違約風險之證券(公司債與股票)乃是公司價值之衍生性商品,無法以傳統資產配置對股票與債券部位採取現貨方式處理最適投資策略,在此必需同時結合財務工程處理衍生性金融商品計價與避險之技術來解決。本研究利用Kron & Kraft (2003) 彈性求解法來針對市場是否有投資限制、債券提前違約、到期違約及利率隨機與否等假設,基於不同投資組合情境分析來最適投資部位策略。本研貢獻和究創新突破之處在於特別探討公司違約時,債券投資人不再享有全部公司殘值之求償權,此時股東亦享有部份比例之求償權,違約後之公司殘值將由債券投資人與股東兩者比例共分之特殊情境下,對數型態財富效用之投資人對於提前違約風險之接受度高於到期違約風險,若一般情境(股東無任何求償權)則為相反。此外亦特別提供最適成長投資組合之動態避險策略封閉解,藉以提供投資人面臨企業違約風險時應制定之投資決策與動態調整,使本研究臻至週延與實用。zh_TW
dc.description.abstract (摘要) Under the Merton (1969) optimal portfolio problem, we only consider the specific investor, whose wealth utility follows the type of logarithm function; wants to maximize the expected value of the terminal wealth utility through determine the optimal investment strategy in advance. He divides his wealth into the riskless asset and risky assets such as the money market account and the various-risky securities issued by the corporate.

Based on the Merton firm value framework (1974), the defaultable securities, such as the corporate bonds and stocks, are the derivatives instruments of the firm value. It will be inappropriate if we deal with this optimal portfolio problem under the original methods. Therefore, we need to handle this optimal asset allocation problem through the pricing, valuation and hedging techniques from the financial engineering simultaneously.

This study apply the elasticity approach to portfolio optimization (EAPO, Kraft ,2003) to solve the optimal portfolio strategy under various scenarios, such as the market contains the investment constrain or not, intermediate default risks, mature default risk, interest rate risky under the stochastic process.

The innovation and contribution of this paper are especially breaking the common setting and analysis the optimal-growth-portfolio strategy under the special scenario. In the common setting, as soon as the default event occurs, the residual firm value will be claimed by the corporate bondholders with fully proportion and the stockholder cannot share any residual value. Oppositely, the stockholder will be able to share the residual firm value proportionally with the corporate bondholder together under the so-called special scenario. We found that the investor would have higher acceptance of the premature default risk than the mature default risk in the special scenario. This phenomenon will be reversed under the common scenario.

Furthermore, in order to make this study more completely and useful, we do not only illustrate the optimal investment strategy but also provide the closed-formed solution of the dynamic hedge strategy of the risky position, composed by the defaultable securities. This could help the optimal-growth-portfolio-oriented investor to make investment decision while they face the firm value downward decreasing.
en_US
dc.description.tableofcontents 第一章 緒論 ………………………………………………………………………4
第二章 投資組合情境與金融市場設定
第一節 投資組合資產內容……………………………………………………….9
第二節 金融市場設定……………………………………………………………10
第三章 Merton (1974) 公司價值理論及債券計價模型………………………13
第四章 僅有「到期違約」風險之最適投資策略
第一節 無投資限制之下的最適投資策略………………………………………17
第二節 有投資限制之下的最適投資策略………………………………………24
第五章 存有「違約風險」及「利率風險」之最適投資策略
第一節 相關證券計價模型與避險參數…………………………………………28
第二節 股東有求償權之下的最適投資策略……………………………………33
第六章 相關參數試算結果及財務意涵解釋
第一節 模型計算流程與架構說明………………………………………………38
第二節 衍生性證券之價格及敏感度分析………………………………………39
第三節 「期望值」觀點下之最適投資策略試算分析…………………………42
第四節 「模擬值」觀點下之最適投資策略試算分析…………………………46
第七章 最適成長投資組合之動態避險策略……………………………………50
第八章 結論與建議………………………………………………………………56

附錄
附錄A 回顧利用彈性與存續期間求最適投資策略之方法(EAPO法) ……………………58
附錄B Briys–de Varenne (1997) 債券計價模型之拆解與重組………………………62
附錄C Briys–de Varenne (1997) 股票計價模型之拆解與重組………………………63
附錄D 回顧Vasicek模型之零息債券計價公式以及對應之存續期間……………………64
附錄E 公司價值與即期利率之關係 ………………………………………………………65
附錄F Briys–de Varenne (1997)債券與股票的避險參數(Delta)和彈性……………70
附錄G Briys–de Varenne (1997)債券與股票避險參數(Rho)和存續期間……………72
附錄 H 公司價值觀點下選擇權之標準常態機率值的說明………………………………74
附錄 I 最適控制變元以及最適投資組合策略之求解過程說明…………………………81

表目錄
表4-1各種不同部位的「價格彈性」定義……………………………………………….20
表5-1 Black-Cox (1976) 公司債券評價模型於債券到期日的部位拆解說明……….29
表5-2-1 特殊情境下,公司債於公司債到期日的現金流量部位拆解說明……………30
表5-2-2 特殊情境下,股票於公司債到期日的現金流量部位拆解說明………………31
表6-1 外生參數與內生參數說明表………………………………………………………38
表6-3 特殊情境與一般情境之最適資產配置策略比較…………………………………45

圖目錄
圖1-1 Merton (1969)「隨機控制法」與Kraft (2003)「彈性求解法」比較示意圖……5
圖3-1 公司債券、股東價值與公司價值於債券到期日的關係……………………………15
圖6-1 模型計算流程示意圖…………………………………………………………………39
圖6-2-1 利用蒙地卡羅模擬標的資產(公司價值)之實際表現……………………………39
圖6-2-2 投資期間內每一期之證券價格期望值……………………………………………40
圖6-2-3 時間與初始公司價值對證券價格及避險參數之變化影響………………………41
圖6-2-4 初始公司價值與公司價值波動度對證券價格及避險參數之影響………………41
圖6-2-5 時間與初始利率對於證券避險參數的變化影響…………………………………41
圖6-3-1 投資期間內每期最適資產配置結果變化圖..……………………………………42
圖6-3-2 提前違約時債券投資人可得殘值比例(f1)對證券價格及投資策略之影響……43
圖6-3-3 到期違約時債券投資人可得殘值比例(f2)對證券價格及投資策略之影響……44
圖6-3-4 違約時債券投資人求償比例(f1與f2)對最適投資策略之影響…………………45
圖6-4-1 投資期間內每一期之證券價格模擬值.………………………………………….46
圖6-4-2 投資期間內每一期之資產配置模擬值.………………………………………….47
圖6-4-3 投資期間內每一期之證券價格模擬值.………………………………………….48
圖6-4-4 投資期間內每一期之資產配置模擬值.………………………………………….49
圖7-1 債券投資人報償收益示意圖…………………………………………………………51
圖7-2 股東報償收益示意圖…………………………………………………………………52
圖7-3 公司價值與投資人財富值模擬圖……………………………………………………55
圖7-4 避險策略模擬圖………………………………………………………………………55
圖H-1-1 歐式買權(一):股東價值於債券到期日T之示意圖…………………………….74
圖H-1-2 歐式賣權(一):債券投資人收益於債券到期日T之示意圖…………………….75
圖H-2-1 歐式買權(二):股東價值於債券到期日T之示意圖…………………………….76
圖H-2-2 歐式賣權(二):債券投資人收益於債券到期日T之示意圖…………………….77
圖H-3-1 歐式買權(三):股東價值於時間t之示意圖…………………………………….79
圖H-3-2 歐式賣權(三):債券投資人收益於時間t之示意圖…………………………….79

參考文獻 (Reference)………………………………………………………………………84
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0933580101en_US
dc.subject (關鍵詞) 最適投資組合zh_TW
dc.subject (關鍵詞) 信用風險zh_TW
dc.subject (關鍵詞) 違約風險zh_TW
dc.subject (關鍵詞) 彈性zh_TW
dc.subject (關鍵詞) 存續期間zh_TW
dc.subject (關鍵詞) Optimal portfoliosen_US
dc.subject (關鍵詞) credit risken_US
dc.subject (關鍵詞) default risken_US
dc.subject (關鍵詞) elasticityen_US
dc.subject (關鍵詞) durationen_US
dc.title (題名) 具有違約風險證券之最適投資組合策略zh_TW
dc.title (題名) Optimal Portfolios with Default Risks ─ A Firm Value Approachen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) ________________________________________zh_TW
dc.relation.reference (參考文獻) [01] Black, F., and J. C. Cox, 1976, Valuing corporate securities: Some effects of bond indenture provisions, Journal of Finance 31: 351-367.zh_TW
dc.relation.reference (參考文獻) [02] Black, F.; and M. Scholes, 1973, The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81: 637-654.zh_TW
dc.relation.reference (參考文獻) [03] Briys, E., and F. de Varenne, 1997, Valuing risky fixed rate debt: An extension, Journal of Financial and Quantitative Analysis 32: 239-248.zh_TW
dc.relation.reference (參考文獻) [04] Geske, R., 1977, The valuation of corporate liabilities as compound options, Journal of Financial and Quantitative Analysis 12: 541-552.zh_TW
dc.relation.reference (參考文獻) [05] Hull, J. C., and A. White, 1995, The impact of default risk on the prices of options and other derivative securities, Journal of Banking and Finance 19: 299-322.zh_TW
dc.relation.reference (參考文獻) [06] Johnson, H., and R. Stulz, 1987, The pricing of options with default risk, Journal of Finance 42: 267-280.zh_TW
dc.relation.reference (參考文獻) [07] Karatzas, I., J. P. Lehoczky., and S. E. Shreve, 1987, Optimal portfolio and consumption decisions for a small investor on a finite horizon, SIAM Journal on Control and Optimization 27: 1157-1186.zh_TW
dc.relation.reference (參考文獻) [08] Kraft, H., 2003, The elasticity approach to portfolio optimization, Mathematical Methods of Operations Research (ZOR) 58: 159–182.zh_TW
dc.relation.reference (參考文獻) [09] Korn, R., and H. Kraft, 2003, Optimal Portfolios with Defaultable Securities: A Firm Value Approach, International Journal of Theoretical and Applied Finance 6: 793-819.zh_TW
dc.relation.reference (參考文獻) [10] Longstaff., and Schwartz, 1995, A simple approach to valuing risky fixed and floating rate debt, Journal of Finance 50: 789-819.zh_TW
dc.relation.reference (參考文獻) [11] Merton, R. C., 1969, Lifetime portfolio selection under uncertainty: the continuous case, Reviews of Economical Statistics 51: 247-257.zh_TW
dc.relation.reference (參考文獻) [12] Merton, R. C., 1971, Optimal consumption and portfolio rules in a continuous-time model, Journal of Economic Theory 3: 373-413.zh_TW
dc.relation.reference (參考文獻) [13] Merton, R. C., 1974, On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance 29: 449-479.zh_TW
dc.relation.reference (參考文獻) [14] Saa-Requejo, J., and Santa-Clara, P, 1999, Bond pricing with default risk, Working paper, UCLA.zh_TW
dc.relation.reference (參考文獻) [15] Vasicek, O, 1977, An equilibrium characterization of the term structure, Journal of Financial Economics 5: 177-188.zh_TW
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