Elucidating Asymmetric Volatility in Asset Returns and Optimizing Portfolio Choice Using Time-Changed Lévy Processes

運用時間轉換Lévy過程探究資產報酬波動度不對稱及最適投資組合理論

陳正暉(Chen Zheng-Hui) ； 廖四郎(Liao Szu-Lang)

《財務金融學刊》 18卷2期 (2010/06) Pp. 135-166

https://doi.org/10.6545/JFS.2010.18(2).5

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。

關鍵字

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

並列摘要

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 purecontinuous 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 infiniteactivity jump structure.

並列關鍵字

Optimal portfolio choice ； stochastic volatility ； time-changed Lévy processes ； leverage effect ； volatility feedback effect ； asymmetric volatility

參考文獻

Ané, T.,Geman, H.(2000).Order Flow, Transaction Clock, and Normality of Asset Returns.Journal of Finance.55,2259-2284.

Barndorff-Nielsen, O(1998).Processes of Normal Inverse Gaussian Type.Finance and Stochastics.2,41-68.

Bekaert, G.,Wu, G.(2000).Asymmetric Volatility and Risk in Equity Markets.Review of Financial Studies.13,1-42.

Benth, F.,Karlsen, K.,Reikvam, K.(2001).A Note on Portfolio Management under Non-Gaussian Logreturns.International Journal of Theoretical and Applied Finance.4,711-732.

Black, F.(1976).Studies of Stock Price Volatility Changes.Meeting of the American Statistical Association, Business and Economical Statistics Section.(Meeting of the American Statistical Association, Business and Economical Statistics Section).