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題名 資產報酬率波動度不對稱性與動態資產配置
Asymmetric Volatility in Asset Returns and Dynamic Asset Allocation
作者 陳正暉
Chen,Zheng Hui
貢獻者 廖四郎
Liao,Szu Lang
陳正暉
Chen,Zheng Hui
關鍵詞 最適投資組合
隨機波動度
時間轉換Lévy過程
槓桿效果
波動度回饋效果
波動度不對稱
Optimal portfolio choice
stochastic volatility
time-changed Lévy processes
leverage effect
volatility feedback effect
asymmetric volatility
日期 2009
上傳時間 8-十二月-2010 16:08:12 (UTC+8)
摘要 本研究顯著地發展時間轉換Lévy過程在最適投資組合的運用性。在連續Lévy過程模型設定下,槓桿效果直接地產生跨期波動度不對稱避險需求,而波動度回饋效果則透過槓桿效果間接地發生影響。另外,關於無窮跳躍Lévy過程模型設定部分,槓桿效果仍扮演重要的影響角色,而波動度回饋效果僅在短期投資決策中發生作用。最後,在本研究所提出之一般化隨機波動度不對稱資產報酬動態模型下,得出在無窮跳躍的資產動態模型設定下,擴散項仍為重要的決定項。
This study significantly extends the applicability of time-changed Lévy processes to the portfolio optimization. The leverage effect directly induces the intertemporal asymmetric volatility hedging demand, while the volatility feedback effect exerts a minor influence via the leverage effect under the pure-continuous time-changed Lévy process. Furthermore, the leverage effect still plays a major role while the volatility feedback effect just works over the short-term investment horizon under the infinite-jump Lévy process. Based on the proposed general stochastic asymmetric volatility asset return model, we conclude that the diffusion term is an essential determinant of financial modeling for index dynamics given infinite-activity jump structure.
參考文獻 Ané, T., and H. Geman, 2000, "Order Flow, Transaction Clock, and Normality of Asset Re-turns." Journal of Finance 55, 2259-2284.
Applebaum, D, 2004, Lévy processes and stochastic calculus (Cambridge Univ Press).
Barndorff-Nielsen, O, 1998, "Processes of Normal Inverse Gaussian type." Finance and Sto-chastics 2, 41-68.
Barndorff-Nielsen, O., and N. Shephard, 2001, "Non-Gaussian Ornstein-Uhlenbeck-based mod-els and some of their uses in financial economics." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63, 167-241.
Bekaert, G., and G. Wu, 2000 "Asymmetric volatility and risk in equity markets." Review of Financial Studies 13, 1-42.
Benth, F., K. Karlsen and K. Reikvam, 2001, "A Note on Portfolio Management under Non-Gaussian Logreturns." International Journal of Theoretical and Applied Finance 4, 711-732.
—, 2003, "Merton’s Portfolio Optimization Problem in a Black and Scholes Market with Non-Gaussian Stochastic Volatility." Mathematical Finance 13, 215-244.
Bertoin, J, 1996, Lévy processes (Cambridge Univ Press).
Black, F., 1976, "Studies of stock price volatility changes." In Meeting of the American Statistical Association, Business and Economical Statistics Section.
Campbell, J. Y. and L. Hentschel, 1992, ‘’No News is Good News. An Asymmetric Model of Changing Volatility in Stock Return.’’ Journal of Financial Economics 31, 281-318.
Campbell, J., A. Lo, and A. MacKinlay, 1997, The Econometrics of Financial Markets (Prince-ton University Press).
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.
—, 2003, "Stochastic Volatility for Lévy Processes." Mathematical Finance 13, 345-382.
Carr, P., and L. Wu, 2004, "Time-changed Lévy Processes and Option Pricing." Journal of Fi-nancial Economics 71, 113-141.
—, 2007, "Stochastic Skew in Currency Options." Journal of Financial Economics 86, 213-247.
—, 2008 "Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions: Disen-tangling the Multi-Dimensional s in S&P 500 Index Options." Working Paper.
Cartea, Á., and S. Howison, 2003, Distinguished limits of Lévy-Stable processes, and applica-tions to option pricing: Mathematical Institute, University of Oxford,.
Chacko, G., and L. Viceira, 2005, "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets." Review of Financial Studies 18, 1369-1402.
—, 2003, "Spectral GMM estimation of continuous-time processes." Journal of Econometrics 116, 259-292.
Chernov, M., A. Ronald Gallant, E. Ghysels and G. Tauchen, 2003, "Alternative models for stock price dynamics." Journal of Econometrics 116, 225-257.
Christie, A, 1982, "The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects." Journal of Financial Economics 10, 407-432.
Chung, C. F., B. S. Kuo and C. Y. Yeh, 2008, "How does the Volatility Feedback Effect Affect Asymmetric Volatility and Dynamic Asset Allocation." Working Paper.
Chunhachinda, P., K. Dandapani, S. Hamid and A. Prakash, 1997, "Portfolio Selection and Skewness: Evidence from International Stock Markets." Journal of Banking & Finance 21, 143-168.
Clark, P, 1973, "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices." Econometrica 41, 135-155.
Cont, R, 2001, "Empirical properties of asset returns: stylized facts and statistical issues." Quan-titative Finance 1, 223-236.
Cont, R., and P. Tankov, 2004, Financial Modelling with Jump Processes (CRC Press).
Cox, J., J. Ingersoll Jr, and S. Ross, 1985, "A Theory of the Term Structure of Interest Rates." Econometrica 53, 385-407.
Cvitanić, J., V. Polimenis and F. Zapatero, 2008, "Optimal Portfolio Allocation with Higher Moments." Annals of Finance 4, 1-28.
Duffie, D., J. Pan and K. Singleton, 2000, "Transform Analysis and Asset Pricing for Affine Jump-diffusions." Econometrica 68, 1343-1376.
Eberlein, E., and U. Keller, 1995, "Hyperbolic Distributions in Finance." Bernoulli 281-299.
Engle, R, 1982, "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation." Econometrica 50, 987-1007.
Fama, E. F, 1965, "The Behavior of Stock-market Prices." Journal of Business 38, 34-105.
Geman, H, 2002, "Pure Jump Lévy Processes for Asset Price Modelling." Journal of Banking & Finance 26, 1297-1316.
—, 2005, "From Measure Changes to Time Changes in Asset Pricing." Journal of Banking &Finance 29, 2701-2722.
Geman, H. and T. Ané, 1996, "Stochastic Subordination." Risk 9, 145-149.
Geman, H., D. Madan and M. Yor, 2001, "Time Changes for Lévy Processes." Mathematical Finance 11, 79-96.
Gron, A., B. Jørgensen and N. Polson, 2004, "Optimal Portfolio Choice and Stochastic Volatili-ty." Working Paper.
Huang, J. and L. Wu, 2004, "Specification analysis of option pricing models based on time-changed Lévy processes." Journal of Finance 59, 1405-1439.
Jacob, J. and A. Shiryaev, 2003, Limit Theorems for Stochastic Processes, 2nd (Berlin: Sprin-ger-Verlag).
Jondeau, E., S. Poon and M. Rockinger, 2007, Financial Modeling under Non-Gaussian Distri-butions (Springer Verlag).
Kallsen, J, 2000, "Optimal Portfolios for Exponential Lévy Processes." Mathematical Methods of Operations Research 51, 357-374.
Karatzas, I. and S. Shreve, 1991, Brownian motion and stochastic calculus (Springer).
Kraus, A. and R. Litzenberger, 1976, "Skewness Preference and the Valuation of Risk Assets." Journal of Finance 1085-1100.
Liu, J, 2007, "Portfolio Selection in Stochastic Environments." Review of Financial Studies 20, 1-39.
Liu, J., F. Longstaff and J. Pan, 2003, "Dynamic Asset Allocation with Event Risk." Journal of Finance 231-259.
Ma, J., and J. Yong, 1999, Forward-backward Stochastic Differential Equations and Their Ap-plications: Differential Equations and Their Applications (Springer Verlag).
Madan, D., P. Carr and E. Chang, 1998, "The variance gamma process and option pricing." Eu-ropean Finance Review 2, 79-105.
Madan, D., and E. Seneta, 1990, "The Variance Gamma (VG) Model for Share Market Returns." Journal of Business 63, 511-524.
Madan, D. and M. Yor, 2008, "Representing CGMY and Meixner Lévy Processes as Time Change Brownian Motions." Journal of Computational Finance 12, 27-47.
Mandelbrot, B, 1963, "The of Certain Speculative Prices." Journal of Business 36, 394-419.
Mendoza, R., P. Carr and V. Linetsky, 2008, "Time Changed Markov Processes in Unified Cre-dit-Equity Modeling." Mathematical Finance, forthcoming.
Merton, R, 1971, "Optimum Consumption and Portfolio Rules in a Continuous-time Model." Journal of Economic Theory 3, 373–413.
Mo, H. and L. Wu, 2007, "International Capital Asset Pricing: Theory and Evidence from Index Options." Journal of Empirical Finance 14, 465-498.
Monroe, I, 1978, "Processes that Can Be Embedded in Brownian Motion." Annals of Probability 6, 42-56.
Nelson, D, 1991, "Conditional Heteroskedasticity in Asset Returns: A New Approach." Econo-metrica 59, 347-370.
Nunno, G., T. Meyer-Brandis, B. Øksendal and F. Proske, 2006, "Optimal Portfolio for an In-sider in a Market Driven by Lévy processes." Quantitative Finance 6, 83-94.
Øksendal, B. and A. Sulem, 2005, Applied Stochastic Control of Jump Diffusions (Sprin-ger-Verlag Berlin Heidelberg).
Rydberg, T, 1999, "Generalized Hyperbolic Diffusion Processes with Applications in Finance." Mathematical Finance 9, 183-201.
Sato, K, 1999, Lévy processes and infinitely divisible distributions (Cambridge Univ Press).
Wachter, J, 2002, "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets." Journal of Financial and Quantitative Analysis 37, 63-91.
Wu, G, 2001, "The Determinants of Asymmetric Volatility." Review of Financial Studies 14, 837-859.
Wu, L, 2003, "Jumps and Dynamic Asset Allocation." Review of Quantitative Finance and Ac-counting 20, 207-243.
—, 2006 "Dampened Power Law: Reconciling the Tail Behavior of Financial Asset Returns." Journal of Business 79, 1445-1474.
—, 2008, "Modeling financial security returns using Lévy processes." In Handbook of Financial Engineering, J. Birge and V. Linetsky, eds. Elsevie
描述 博士
國立政治大學
金融研究所
93352510
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0093352510
資料類型 thesis
dc.contributor.advisor 廖四郎zh_TW
dc.contributor.advisor Liao,Szu Langen_US
dc.contributor.author (作者) 陳正暉zh_TW
dc.contributor.author (作者) Chen,Zheng Huien_US
dc.creator (作者) 陳正暉zh_TW
dc.creator (作者) Chen,Zheng Huien_US
dc.date (日期) 2009en_US
dc.date.accessioned 8-十二月-2010 16:08:12 (UTC+8)-
dc.date.available 8-十二月-2010 16:08:12 (UTC+8)-
dc.date.issued (上傳時間) 8-十二月-2010 16:08:12 (UTC+8)-
dc.identifier (其他 識別碼) G0093352510en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49661-
dc.description (描述) 博士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) 93352510zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 本研究顯著地發展時間轉換Lévy過程在最適投資組合的運用性。在連續Lévy過程模型設定下,槓桿效果直接地產生跨期波動度不對稱避險需求,而波動度回饋效果則透過槓桿效果間接地發生影響。另外,關於無窮跳躍Lévy過程模型設定部分,槓桿效果仍扮演重要的影響角色,而波動度回饋效果僅在短期投資決策中發生作用。最後,在本研究所提出之一般化隨機波動度不對稱資產報酬動態模型下,得出在無窮跳躍的資產動態模型設定下,擴散項仍為重要的決定項。zh_TW
dc.description.abstract (摘要) This study significantly extends the applicability of time-changed Lévy processes to the portfolio optimization. The leverage effect directly induces the intertemporal asymmetric volatility hedging demand, while the volatility feedback effect exerts a minor influence via the leverage effect under the pure-continuous time-changed Lévy process. Furthermore, the leverage effect still plays a major role while the volatility feedback effect just works over the short-term investment horizon under the infinite-jump Lévy process. Based on the proposed general stochastic asymmetric volatility asset return model, we conclude that the diffusion term is an essential determinant of financial modeling for index dynamics given infinite-activity jump structure.en_US
dc.description.tableofcontents 1. Introduction 1
2. Time-Changed Lévy Processes with Asymmetric Volatility 8
2.1 Fundamental Properties of Lévy Process 8
2.2 Stochastic Time Changes for Lévy Processes 10
2.3 Time-Changed Asset Price Processes with Asymmetric Volatility 12
2.3.1 Pure-Continuous Asset Dynamic Process 14
2.3.2 Infinite-jump Asset Dynamic Process 16
3. Dynamic Asset Allocation 23
3.1 Investment Opportunity Set and Investor Preference 23
3.2 Pure-Continuous Asset Dynamic Process 25
3.2.1 Numerical Examples 28
3.3 Infinite-Jump Asset Dynamic Process 34
3.3.1 Reduced Time-Changed Lévy Process 39
3.3.2 Numerical Examples 42
4. Empirical Results 48
4.1 The General Stochastic Asymmetric Volatility Model 48
4.2 Data and Model Parameter Estimation 50
5. Concluding Remarks 60
References 63
Appendices 69
zh_TW
dc.format.extent 589263 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0093352510en_US
dc.subject (關鍵詞) 最適投資組合zh_TW
dc.subject (關鍵詞) 隨機波動度zh_TW
dc.subject (關鍵詞) 時間轉換Lévy過程zh_TW
dc.subject (關鍵詞) 槓桿效果zh_TW
dc.subject (關鍵詞) 波動度回饋效果zh_TW
dc.subject (關鍵詞) 波動度不對稱zh_TW
dc.subject (關鍵詞) Optimal portfolio choiceen_US
dc.subject (關鍵詞) stochastic volatilityen_US
dc.subject (關鍵詞) time-changed Lévy processesen_US
dc.subject (關鍵詞) leverage effecten_US
dc.subject (關鍵詞) volatility feedback effecten_US
dc.subject (關鍵詞) asymmetric volatilityen_US
dc.title (題名) 資產報酬率波動度不對稱性與動態資產配置zh_TW
dc.title (題名) Asymmetric Volatility in Asset Returns and Dynamic Asset Allocationen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Ané, T., and H. Geman, 2000, "Order Flow, Transaction Clock, and Normality of Asset Re-turns." Journal of Finance 55, 2259-2284.zh_TW
dc.relation.reference (參考文獻) Applebaum, D, 2004, Lévy processes and stochastic calculus (Cambridge Univ Press).zh_TW
dc.relation.reference (參考文獻) Barndorff-Nielsen, O, 1998, "Processes of Normal Inverse Gaussian type." Finance and Sto-chastics 2, 41-68.zh_TW
dc.relation.reference (參考文獻) Barndorff-Nielsen, O., and N. Shephard, 2001, "Non-Gaussian Ornstein-Uhlenbeck-based mod-els and some of their uses in financial economics." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63, 167-241.zh_TW
dc.relation.reference (參考文獻) Bekaert, G., and G. Wu, 2000 "Asymmetric volatility and risk in equity markets." Review of Financial Studies 13, 1-42.zh_TW
dc.relation.reference (參考文獻) Benth, F., K. Karlsen and K. Reikvam, 2001, "A Note on Portfolio Management under Non-Gaussian Logreturns." International Journal of Theoretical and Applied Finance 4, 711-732.zh_TW
dc.relation.reference (參考文獻) —, 2003, "Merton’s Portfolio Optimization Problem in a Black and Scholes Market with Non-Gaussian Stochastic Volatility." Mathematical Finance 13, 215-244.zh_TW
dc.relation.reference (參考文獻) Bertoin, J, 1996, Lévy processes (Cambridge Univ Press).zh_TW
dc.relation.reference (參考文獻) Black, F., 1976, "Studies of stock price volatility changes." In Meeting of the American Statistical Association, Business and Economical Statistics Section.zh_TW
dc.relation.reference (參考文獻) Campbell, J. Y. and L. Hentschel, 1992, ‘’No News is Good News. An Asymmetric Model of Changing Volatility in Stock Return.’’ Journal of Financial Economics 31, 281-318.zh_TW
dc.relation.reference (參考文獻) Campbell, J., A. Lo, and A. MacKinlay, 1997, The Econometrics of Financial Markets (Prince-ton University Press).zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) —, 2003, "Stochastic Volatility for Lévy Processes." Mathematical Finance 13, 345-382.zh_TW
dc.relation.reference (參考文獻) Carr, P., and L. Wu, 2004, "Time-changed Lévy Processes and Option Pricing." Journal of Fi-nancial Economics 71, 113-141.zh_TW
dc.relation.reference (參考文獻) —, 2007, "Stochastic Skew in Currency Options." Journal of Financial Economics 86, 213-247.zh_TW
dc.relation.reference (參考文獻) —, 2008 "Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions: Disen-tangling the Multi-Dimensional s in S&P 500 Index Options." Working Paper.zh_TW
dc.relation.reference (參考文獻) Cartea, Á., and S. Howison, 2003, Distinguished limits of Lévy-Stable processes, and applica-tions to option pricing: Mathematical Institute, University of Oxford,.zh_TW
dc.relation.reference (參考文獻) Chacko, G., and L. Viceira, 2005, "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets." Review of Financial Studies 18, 1369-1402.zh_TW
dc.relation.reference (參考文獻) —, 2003, "Spectral GMM estimation of continuous-time processes." Journal of Econometrics 116, 259-292.zh_TW
dc.relation.reference (參考文獻) Chernov, M., A. Ronald Gallant, E. Ghysels and G. Tauchen, 2003, "Alternative models for stock price dynamics." Journal of Econometrics 116, 225-257.zh_TW
dc.relation.reference (參考文獻) Christie, A, 1982, "The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects." Journal of Financial Economics 10, 407-432.zh_TW
dc.relation.reference (參考文獻) Chung, C. F., B. S. Kuo and C. Y. Yeh, 2008, "How does the Volatility Feedback Effect Affect Asymmetric Volatility and Dynamic Asset Allocation." Working Paper.zh_TW
dc.relation.reference (參考文獻) Chunhachinda, P., K. Dandapani, S. Hamid and A. Prakash, 1997, "Portfolio Selection and Skewness: Evidence from International Stock Markets." Journal of Banking & Finance 21, 143-168.zh_TW
dc.relation.reference (參考文獻) Clark, P, 1973, "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices." Econometrica 41, 135-155.zh_TW
dc.relation.reference (參考文獻) Cont, R, 2001, "Empirical properties of asset returns: stylized facts and statistical issues." Quan-titative Finance 1, 223-236.zh_TW
dc.relation.reference (參考文獻) Cont, R., and P. Tankov, 2004, Financial Modelling with Jump Processes (CRC Press).zh_TW
dc.relation.reference (參考文獻) Cox, J., J. Ingersoll Jr, and S. Ross, 1985, "A Theory of the Term Structure of Interest Rates." Econometrica 53, 385-407.zh_TW
dc.relation.reference (參考文獻) Cvitanić, J., V. Polimenis and F. Zapatero, 2008, "Optimal Portfolio Allocation with Higher Moments." Annals of Finance 4, 1-28.zh_TW
dc.relation.reference (參考文獻) Duffie, D., J. Pan and K. Singleton, 2000, "Transform Analysis and Asset Pricing for Affine Jump-diffusions." Econometrica 68, 1343-1376.zh_TW
dc.relation.reference (參考文獻) Eberlein, E., and U. Keller, 1995, "Hyperbolic Distributions in Finance." Bernoulli 281-299.zh_TW
dc.relation.reference (參考文獻) Engle, R, 1982, "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation." Econometrica 50, 987-1007.zh_TW
dc.relation.reference (參考文獻) Fama, E. F, 1965, "The Behavior of Stock-market Prices." Journal of Business 38, 34-105.zh_TW
dc.relation.reference (參考文獻) Geman, H, 2002, "Pure Jump Lévy Processes for Asset Price Modelling." Journal of Banking & Finance 26, 1297-1316.zh_TW
dc.relation.reference (參考文獻) —, 2005, "From Measure Changes to Time Changes in Asset Pricing." Journal of Banking &Finance 29, 2701-2722.zh_TW
dc.relation.reference (參考文獻) Geman, H. and T. Ané, 1996, "Stochastic Subordination." Risk 9, 145-149.zh_TW
dc.relation.reference (參考文獻) Geman, H., D. Madan and M. Yor, 2001, "Time Changes for Lévy Processes." Mathematical Finance 11, 79-96.zh_TW
dc.relation.reference (參考文獻) Gron, A., B. Jørgensen and N. Polson, 2004, "Optimal Portfolio Choice and Stochastic Volatili-ty." Working Paper.zh_TW
dc.relation.reference (參考文獻) Huang, J. and L. Wu, 2004, "Specification analysis of option pricing models based on time-changed Lévy processes." Journal of Finance 59, 1405-1439.zh_TW
dc.relation.reference (參考文獻) Jacob, J. and A. Shiryaev, 2003, Limit Theorems for Stochastic Processes, 2nd (Berlin: Sprin-ger-Verlag).zh_TW
dc.relation.reference (參考文獻) Jondeau, E., S. Poon and M. Rockinger, 2007, Financial Modeling under Non-Gaussian Distri-butions (Springer Verlag).zh_TW
dc.relation.reference (參考文獻) Kallsen, J, 2000, "Optimal Portfolios for Exponential Lévy Processes." Mathematical Methods of Operations Research 51, 357-374.zh_TW
dc.relation.reference (參考文獻) Karatzas, I. and S. Shreve, 1991, Brownian motion and stochastic calculus (Springer).zh_TW
dc.relation.reference (參考文獻) Kraus, A. and R. Litzenberger, 1976, "Skewness Preference and the Valuation of Risk Assets." Journal of Finance 1085-1100.zh_TW
dc.relation.reference (參考文獻) Liu, J, 2007, "Portfolio Selection in Stochastic Environments." Review of Financial Studies 20, 1-39.zh_TW
dc.relation.reference (參考文獻) Liu, J., F. Longstaff and J. Pan, 2003, "Dynamic Asset Allocation with Event Risk." Journal of Finance 231-259.zh_TW
dc.relation.reference (參考文獻) Ma, J., and J. Yong, 1999, Forward-backward Stochastic Differential Equations and Their Ap-plications: Differential Equations and Their Applications (Springer Verlag).zh_TW
dc.relation.reference (參考文獻) Madan, D., P. Carr and E. Chang, 1998, "The variance gamma process and option pricing." Eu-ropean Finance Review 2, 79-105.zh_TW
dc.relation.reference (參考文獻) Madan, D., and E. Seneta, 1990, "The Variance Gamma (VG) Model for Share Market Returns." Journal of Business 63, 511-524.zh_TW
dc.relation.reference (參考文獻) Madan, D. and M. Yor, 2008, "Representing CGMY and Meixner Lévy Processes as Time Change Brownian Motions." Journal of Computational Finance 12, 27-47.zh_TW
dc.relation.reference (參考文獻) Mandelbrot, B, 1963, "The of Certain Speculative Prices." Journal of Business 36, 394-419.zh_TW
dc.relation.reference (參考文獻) Mendoza, R., P. Carr and V. Linetsky, 2008, "Time Changed Markov Processes in Unified Cre-dit-Equity Modeling." Mathematical Finance, forthcoming.zh_TW
dc.relation.reference (參考文獻) Merton, R, 1971, "Optimum 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) Mo, H. and L. Wu, 2007, "International Capital Asset Pricing: Theory and Evidence from Index Options." Journal of Empirical Finance 14, 465-498.zh_TW
dc.relation.reference (參考文獻) Monroe, I, 1978, "Processes that Can Be Embedded in Brownian Motion." Annals of Probability 6, 42-56.zh_TW
dc.relation.reference (參考文獻) Nelson, D, 1991, "Conditional Heteroskedasticity in Asset Returns: A New Approach." Econo-metrica 59, 347-370.zh_TW
dc.relation.reference (參考文獻) Nunno, G., T. Meyer-Brandis, B. Øksendal and F. Proske, 2006, "Optimal Portfolio for an In-sider in a Market Driven by Lévy processes." Quantitative Finance 6, 83-94.zh_TW
dc.relation.reference (參考文獻) Øksendal, B. and A. Sulem, 2005, Applied Stochastic Control of Jump Diffusions (Sprin-ger-Verlag Berlin Heidelberg).zh_TW
dc.relation.reference (參考文獻) Rydberg, T, 1999, "Generalized Hyperbolic Diffusion Processes with Applications in Finance." Mathematical Finance 9, 183-201.zh_TW
dc.relation.reference (參考文獻) Sato, K, 1999, Lévy processes and infinitely divisible distributions (Cambridge Univ Press).zh_TW
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