考慮價格跳躍不對稱與波動狀態轉換之動態資產配置

Abstract

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。

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.