非線性變幅波動模型族之研究

Abstract

波動性在財務上扮演著關鍵的角色，若能適當的描述波動性模型，將有助於投資組合配置的最適化，進而能有效的控管風險。Chou(2005)將GARCH 模型結合變幅在波動性預測上的優勢進一步提出 CARR(Conditional Auto-Regressive Range)模型，並且在S&P500 股價指數波動性預測實證上獲得優於GARCH模型的結論，因此本論文將以CARR模型為基礎佐以Box-Cox轉換及不對稱性發展出各種不同形式之均數方程式並配適指數(exponential)分配、Log logistic分配、韋伯(Weibull)分配、Gamma分配及一般化 F分配。本文以美國S&P500 指數為主要研究對象進行參數估計，試圖找出S&P500指數是否具有不對稱性以及較佳的均數方程式與分配。實證結果顯示，對稱部分一致以韋伯分配為表現有較好表現，其中以Box-Cox CARR模型為最佳，而不對稱則以對數CARR模型佐以一般化 F分配為S&P 500指數資料的最佳模型。

This paper develops a family of conditional autoregressive range (CARR) models which extends the CARR model of Chou(2005). The nesting relies on a Box-Cox transformation to the conditional range process and a possibly asymmetric shocks impact curve. The asymmetry consists of letting the high/low range depend on the state of the asset price process within fixed time intervals. The estimation of parametric CARR models requires both the choice of a conditional density for range and the specification of a function form for the conditional mean equation. Finally, we assess the practical usefulness of our family of CARR models using S&P500 index data. The results warrant the extra flexibility provided either by the Box-Cox transformation or by the asymmetric response to shocks. Actually, inspecting the parameter estimates of the different specifications reveals that imposing concavity in the shocks impact curve is pivot. The Box-Cox transformation and the asymmetric response to shocks indeed work, to some extent, as substitutes. In particular, the symmetric Box-Cox CARR with weibull distribution and the asymmetric logarithmic CARR models with generalized F distribution produce the best fit.