Elucidating Asymmetrical Volatility in Asset Returns and Optimizing Portfolio Choice Using Time-Changed Levy Processes

Abstract

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.

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。