臺灣博碩士論文加值系統

本論文主要研究在隨機波動度下，當套利者面對套利機會時，套利者會如何決定自身的最適動態投資決策，本文得到套利者會隨著套利機會的大小而調整投資套利資產的比重；同時，若考慮財富限制下，套利者可能會採取部份投資行為，並主要去討論套利者的資本不足所產生的「財富效果｣現象。
而在數學模型部份，我們假設隨著波動度增加，在套利過程中會產生擴大現象，因此在數值分析中，分別考慮固定波動度、隨機波動度、固定風險溢酬係數與動態風險溢酬係數的情況下，我們可以找出套利價值與波動度之間的變動關係，得到套利價值在波動度的敏感程度較大時，可能很容易產生套利價值僵固性的現象。

The main purpose of the thesis is that in the stochastic volatility state when arbitrageurs face the arbitrage opportunities , they will decide their optimal dynamic portfolio strategy . We obtain the conclusion that arbitrageurs would adjust the weight with the value of arbitrage portfolio , and they find it optimal to underinvest in the arbitrage by taking a smaller position than collateral constraints allow . Furthermore, we discuss the existence of the Wealth effect , the main cause of the Wealth effect is that arbitrageurs are short of their capital .
In the theoretical model , we assume that as the volatility increases , we find that there is an amplification phenomenon in the arbitrage . In the numerical analysis , under different conditions, such as constant volatility , stochastic volatility , constant risk premium and dynamic risk premium , we also find the relation between the value of arbitrage portfolio and the volatility .When the sensitivity of the volatileity is large enough , there may exist the rigidity of the value of arbitrage portfolio .

目 錄

謝詞………………………………………………………i
中文摘要…………………………………………………ii
英文摘要......................................iii
目錄..........................................iv
圖次...........................................v

第一章 緒論.................................1
1.1 論文動機.................................1
1.2 研究目的.................................3
1.3 研究架構.................................5
第二章 文獻回顧 ............................6
2.1 套利的限制...............................6
2.2 有關財富效果的文獻討論...................8
2.2.1 單一市場的擴大效應.....................8
2.2.2 跨市場的擴大效應而導致金融瘟疫.........10
2.3 關於部分投資與時間風險之套利限制的文章...11
2.3.1 部份投資的套利行為.....................11
2.3.2 時間風險...............................14

第三章 模型設定與分析結果....................15
3.1 模型架構.................................15
3.2 不考慮財富限制下的最適投資策略...........16
3.3 面對保證金約束下的最適投資策略...........24
3.4 本章小結.................................28

第四章 數值分析..............................32
4.1 模型架構.................................32
4.2 考慮風險溢酬係數為零及波動度為固定值.....34
4.3 考慮固定風險溢酬係數及隨機波動度.........38
4.4 考慮動態風險溢酬係數及隨機波動度.........44
4.5 本章小結.................................48

第五章 結論與未來研究方向....................51
5.1 論文結論.................................51
5.1 未來研究方向.............................51

附錄一........................................53
參考文獻......................................57

參考文獻：
Abreu , D. , Brunnermeier , M. ,2002 ,” Synchronization risk and delayed arbitrage ”, Journal of Financial economics ,66 ,341-360 .
Bernardo A.E. , Ledoit O. ,2000 ,” Gain, loss, and asset pricing “ , Journal of Political Economy ,108(1) , 144-172.
Chang , F.R. ,2004 , “Stochastic optimization in continuous time ”, Cambridge, UK .
Cochrane , J.H. ,Saa-Requejo ,J. ,2000, “Beyond Arbitrage :Good-deal asset price bounds in incomplete markets “, Journal of Political Economy ,108(1) , 79-119 .
Gromb ,D. ,Vayanos , D. 2002 ,“Equilibrium and welfare in markets with financially constrained arbitrageurs ”, Journal of Financial economics , 66 ,361-407 .
Hull ,J.C. , White A.., 1987 ,“ The Pricing of Options On Assets with Stochastic Volatilities “, Journal of Finance , 42 , 281-300 .
Heston ,S.L. , 1993, ”A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options “,Review of Financial Studies, v6 , n2 ,327-343 .
Liu , J., 2000, “Portfolio Selection in Stochastic Environments”, Working paper, UCLA.
Liu , J., Longstaff , F.A., 2004a, “Risk and Return in Fixed Income Arbitrage :Nickels in front of a Steamroller?”, Working paper, UCLA.
Liu , J., Longstaff , F.A., 2004b, “Losing Money on Arbitrage :Optimal Dynamic Portfolio Choice in Market with Arbitrage Opportunities”, Review of Financial Studies , 17 ,611-641.
Longstaff ,F.A. , Schwartz, E.S. , 1992, ”Interest Rate Volatility and the Term Structure : A Two-Factor General Equilibrium Model “, Journal of Finance , 47 ,1259-1282.
Krishnamurthy, A. ,2002 , “The bond/old-bond spread “, Journal of Financial economics , 66 ,463-506 .
Kyle , A.S. , Xiong ,W., 2001 , “Contagion as wealth effect “ , Journal of Finance , 56(4) , 1401-1440 .
Merton , R .,1971 , “Optimum Consumption and Portfolio Rules in a Continuous Time Model “, Journal of Economic Theory , 3, 373-413.
Merton , R., 1990 , “Continuous Time Finance”, Basil Blackwell, Cambridge, MA.
Shleifer , A. , Vishny R. W. ,1997 ,” The Limits of Arbitrage”, Journal of Finance , 52(1) , 35-55.
Xiong ,W. , 2001 , “Convergence trading with wealth effects : an amplification mechanism in financial markets.” , Journal of Financial economics , 62(2) , 247-292 .