题名

考慮價格跳躍不對稱與波動狀態轉換之動態資產配置

并列篇名

Dynamic Asset Allocation Concerning Asymmetric Price Jumps and Volatility State Switch

作者

蘇恩德(En-Der Su)

关键词

動態規劃 ； 跳躍擴散隨機過程 ； 事件風險 ； 修正尤拉法 ； 投資績效 ； Dynamic Programming ； Jump-diffusion Stochastic Process ； Event Risk ； Modified Euler Method ； Investment Performance

期刊名称

管理與系統

卷期/出版年月

18卷1期（2011 / 01 / 01）

页次

1 - 33

内容语文

繁體中文
中文摘要

動態隨機規劃模型須納入價格或波動的隨機過程以求解動態效用函數最適化問題。價格與波動隨機過程的應用尚須考慮市場普遍存有的非線性現象，例如，價格或波動的跳空、不對稱以及狀態轉換等。因此本文修正價格與波動雙跳躍隨機微分方程(stochastic differential equation, SDE)模型另提出數個價格不對性或（且）波動狀態轉換的SDE模型並以台股指數(TAIEX)檢驗模型間的巢狀關係，結果發現：價格不對性與波動狀態轉換現象顯著存在但波動跳躍的現象極微，雙跳躍模型可修正爲價格跳躍與波動狀態轉換模型。情境分析顯示資產配置比例逐期上升或下降是受價格與波動相關性爲正或負值的影響。以速度、精確、收斂性較佳的修正尤拉數值法來解TAIEX動態資產配置比例；之後，運用此解並比較模型投資績效顯示：合併價格跳躍不對稱與波動狀態轉換效果之修正模型可大幅改善風險趨避程度大（即保守性投資人）、規劃期長的投資績效，但加入單一效果之修正模型的績效無明顯改善。
英文摘要

The stochastic dynamic programming model should be able to consider both price and volatility stochastic processes to solve the problem of optimizing a dynamic utility function. Empirically, it is necessary to take into account potential nonlinear phenomena related to price and volatility, such as jumps, asymmetry and state switch, when applying these stochastic processes. In this paper, the price asymmetry and volatility state switch effects are incorporated separately or jointly into the price and volatility double-jump stochastic differential equation (SDE) in order to create several revised SDE models. The Taiwan stock index (TAIEX) is then used to test the nest hypothesis between the revised models. The test result supports that the price asymmetric and volatility state switch effects are significant but that the volatility jumps are very weak. This leads to the fact that the price asymmetry and volatility state switch SDE model is more reasonable. According to a scenario analysis, whether the dynamic weight would gradually go up or down depends on the sign of correlation between price and volatility. The modified Euler method is used to obtain optimal numerical solutions for the dynamic weight of TAIEX since it has shown better performance in terms of speed, accuracy, and convergence. Using these solutions, the investment performance comparisons between models show that the price asymmetry and volatility state switch adjusted model can substantially improve longer-term and more risk-averse (i.e., conservative) outcomes, and that the single effect adjusted models are unable to do so.
主题分类 基礎與應用科學 > 統計
社會科學 > 財金及會計學
社會科學 > 管理學
参考文献
  1. Bochner, S., “Diffusion Equation and Stochastic Processes,” Proceedings of the National Academy of Science of the United States of America, Vol. 35, No. 7, 1949, pp. 369-370.
  2. Das, S. and Uppal, R., “Systemic Risk and International Portfolio Choice,” Working paper, Santa Clara University, 2001.
  3. Common, E., “Extreme Events and the Role of Learning in Financial Markets,” Working paper, Harvard University, 2000.
  4. Chacko, G. and Viceira, L., “Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets,” Working paper, Harvard University, 2000.
  5. Andersen, T. G.,Benzoni, L.,Lund, J.(2002).An Empirical Investigation of. Continuous-Time Equity Return Models.Journal of Finance,57(3),1239-1284.
  6. Andersen, T. G.,Bollerselev, T.,Diebold, F. X.,Ebens, H.(2001).The Distribution of Realized Stock Return Volatility.Journal of Financial Economics,61(1),43-76.
  7. Arrow, K.(1971).Essays in the Theory of Risk-Bearing.Chicago:Markham Publishing Co..
  8. Baillie, T.(1996).Long Memory Processes and Fractional Integration in Econometrics.Journal of Econometrics,73(1),5-59.
  9. Bakshi, G.,Cao, C.,Chen, Z.(1997).Empirical Performance of Alternative Option Pricing Models.Journal of Finance,52(5),2003-2049.
  10. Ball, C. A.,Torous, W. N.(1983).A Simplified Jump Process for Common Stock Returns.Journal of Financial and Quantitative Analysis,18(1),53-65.
  11. Ball, C. A.,Torous, W. N.(1985).On Jump in Common Stock Prices and Their Impact on Call Pricing.Journal of Finance,40(1),155-173.
  12. Barndorff-Nielsen, O. E.,Shephard, N.(2006).Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation.Journal of Financial Econometrics,4(1),1-30.
  13. Bates, D. S.(1996).Jump and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options.Review of Financial Studies,9(1),69-107.
  14. Bates, D. S.(2000).Post-'87 Crash Fears in SandP 500 Futures Options Markets.Journal of Econometrics,94(1-2),181-238.
  15. Black, F.,Scholes, M.(1973).The Pricing of Options and Corporate Liabilities.Journal of Political Economy,81(3),637-653.
  16. Blundell, R.,Stoker, T. M.(1999).Consumption and the Timing of Income Risk.European Economic Review,43(3),475-507.
  17. Bodurtha, J.,Courtadon, G.(1987).Tests of the American Option Pricing Model in the Foreign Currency Options Market.Journal of Financial and Quantitative Analysis,22(2),297-319.
  18. Brandt, M. W.(1999).Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach.The Journal of Finance,54(5),1609-1645.
  19. Brennan, M. J.,Schwartz, E. S.,Lagnado, R.(1997).Strategic Asset Allocation.Journal of Economic Dynamics and Control,21(8),1377-1403.
  20. Brennan, M. J.,Xia, Y.(2000).Stochastic Interest Rates and Bond-Stock Mix.European Finance Review,4(2),197-210.
  21. Campbell, J.,Cochrane, J.(1999).By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior.Journal of Political Economy,107(2),205-251.
  22. Chou, R. Y.(1988).Volatility Persistence and Stock Valuations: Some Empirical Evidence Using GARCH.Journal of Applied Econometrics,3(4),279-294.
  23. Clark, P. K.(1973).A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices.Econometrica,41(1),135-155.
  24. Constantinides, G.(1990).Habit Formation: A Resolution of the Equity Premium Puzzle.The Journal of Political Economy,98(3),519-543.
  25. Cox, J. C.,Ingersoll, J. E.,Ross, S. A.(1985).A Theory of the Term Structure of Interest Rates.Econometrica,53(2),385-407.
  26. Duffie, D.(2001).Dynamic Asset Pricing Theory.Princeton, NJ:Princeton University Press.
  27. Duffie, D.,Epstein, L. G.(1992).Stochastic Differential Utility.Econometerica,60(2),353-394.
  28. Duffie, D.,Pan, J.(1997).An Overview of Value at Risk.The Journal of Derivatives,4(3),7-49.
  29. Duffie, D.,Pan, J.,Singleton, K.(2000).Transform Analysis and Asset Pricing for Affine Jump Diffusion.Econometrica,68(6),1343-1376.
  30. Eraker, B.,Johannes, M.,Polson, N.(2003).The Impact of Jumps in Volatilities and Returns.Journal of Finance,58(3),1269-1300.
  31. Fama, E. F.(1965).The Behavior of Stock Market Price.Journal of Business,38(1),34-105.
  32. Goldstein, R.,Zapatero, F.(1996).General Equilibrium with Constant Relative Risk Aversion and Vasicek Interest Rates.Mathematical Finance,6(3),331-340.
  33. Grossman, S. J.,Vila, J.-L.(1992).Optimal Dynamic Trading with Leverage Constraints.Journal of Financial and Quantitative Analysis,27(2),151-132.
  34. Han, Y.(2006).Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model.The Review of Financial Studies,19(1),237-271.
  35. Henderson, V.,Hobson, D. G.(2002).Real Options with Constant Relative Risk Aversion.Journal of Economic Dynamics and Control,27(2),329-355.
  36. Herings, P. J.-J.,Kubler, F.(2007).Approximate CAPM When Preferences Are CRRA.Computational Economics,29(1),13-31.
  37. Ingolf, D.,Ernst, M.(2007).Lower Salaries and No Options? On the Optimal Structure of Executive Pay.The Journal of Finance,62(1),303-343.
  38. Jarrow, R. A.,Rosenfeld, E. R.(1984).Jump Risks and the Intertemporal Capital Asset Pricing Model.Journal of Business,57(3),337-351.
  39. Kim, T. S.,Omberg, E.(1996).Dynamic Nonmyopic Portfolio Behavior.Review of Financial Studies,9(1),141-161.
  40. Liu, J.(2007).Portfolio Selection in Stochastic Environments.Review of Financial Studies,20(1),1-39.
  41. Liu, J.,Longstaff, F. A.,Pan, J.(2003).Dynamic Asset Allocation with Event Risk.Journal of Finance,58(1),231-259.
  42. Longstaff, F. A.(2001).Optimal Portfolio Choice and the Valuation of Illiquid Securities.Review of Financial Studies,14(2),407-431.
  43. Lynch, A.(2000).Portfolio Choice and Equity Characteristics: Characterizing the Hedging Demand Induced by Return Predictability.Journal of Financial Economics,62(1),67-130.
  44. Mandelbrot, B. B.(1963).The Variation of Certain Speculative Prices.Journal of Business,36(3),394-419.
  45. Mandelbrot, B. B.(1967).The Variation of Some Other Speculative Prices.Journal of Business,40(3),393-413.
  46. Merton, R.(1992).Continuous-Time Finance.Oxford, UK:Basil Blackwell.
  47. Merton, R.(1969).Lifetime Portfolio Selection under Uncertainty: the Continuous-Time Case.Review of Economics and Statistics,51(3),247-257.
  48. Merton, R.(1976).Option Pricing When Underlying Stock Returns are Discontinuous.Journal of Financial Economics,3(1),125-144.
  49. Merton, R.(1971).Optimal Consumption and Portfolio Rules in a Continuous-Time Model.Journal of Economic Theory,3(4),373-413.
  50. Nelson, C. H.,Escalante, C. L.(2004).Toward Exploring the Location-Scale Condition: A Constant Relative Risk Aversion Location-Scale Objective Function.European Review of Agricultural Economics,31(3),273-287.
  51. Nelson, D. B.(1991).Conditional Heteroskedasticity in Asset Returns: A New Approach.Econometrica,59(2),347-370.
  52. Palacios-Huerta, I.,Serrano, R.(2006).Rejecting Small Gambles under Expected Utility.Economics Letters,91(2),250-259.
  53. Pan, J.(2001).The Jump-Risk Premia Implicit in Option Prices: Evidence from an Integrated Time-Series Study.Journal of Financial Economics,63(1),3-50.
  54. Rabemananjara, R.,Zakolin, J. M.(1993).Threshold ARCH Models and Asymmetries in Volatility.Journal of Applied Econometrics,8(1),31-49.
  55. Saha, A.(1993).Expo-Power Utility: A Flexible Form for Absolute and Relative Risk Aversion.American Journal of Agricultural Economics,75(4),905-913.
  56. Schroder, M.,Skiadas, C.(1999).Optimal Consumption and Portfolio Selection with Stochastic Differential Utility.Journal of Economic Theory,89(1),68-126.
  57. Scott, D. W.(1992).Multivariate Density Estimation: Theory, Practice, and Visualization.NY:John Wiley and Sons.
  58. Sharpe, W. F.(1964).Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.Journal of Finance,19(3),425-442.
  59. Sundaresan, S.(1989).Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth.Review of Financial Studies,2(1),73-89.
  60. Wu, L.(2003).Jumps and Dynamic Asset Allocation.Review of Quantitative Finance and Accounting,20(3),207-243.
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