多變量變幅波動模型的理論與應用

Abstract

本文提出多變量的動態變幅（range）波動模型，並探討其在財務相關議題的應用，內容主要分成三個部分。第一部份提出以變幅為基礎的動態條件相關係數（dynamic conditional correlation，DCC）模型，簡稱為range-based DCC模型，其結合DCC模型以及條件變幅波動（conditional autoregressive range，CARR）模型在波動性預測方面的優勢，藉此改善共變異數矩陣估計的準確性，並且以S&P 500股價指數和10年期的債券期貨做為樣本，進行樣本內和樣本外共變異數預測能力的比較，實證結果指出，在所建立的已實現變異數（realized covariance）指標下，range-based DCC模型表現優於文獻上常見之報酬為基礎的波動模型（包含MA100、EWMA、CCC、BEKK和DCC模型）。第二部分則是基於平均數-共變異數的架構下，結合效用函數，驗證range-based DCC模型之波動擇時的經濟價值，實證結果支持此模型具有顯著的經濟價值，並且更勝於以報酬為基礎的DCC模型。第三部分則是以range-based CCC和range-based DCC模型計算最小變異數的避險比例（minimum variance hedge ratio），並且應用在商品期貨的避險，透過所選用15種商品（包含股價指數、匯率、金屬、農產品、軟性商品和能源市場）的驗證，得知變幅為基礎的波動模型可以有效改善避險績效，並且明顯優於其他以報酬為基礎的波動模型（包含OLS、rollover OLS、CCC和DCC模型）。

This dissertation is intended as an investigation of dynamic range volatility models. There are three main parts in this study. In the first part, we propose a range-based DCC model combined by the return-based DCC model and the CARR model. The substantial gain in efficiency of volatility estimation can boost the accuracy for estimating time-varying covariances. As to the empirical study, we use the S&P 500 stock index and the 10-year treasury bond futures to examine both in-sample and out-of-sample results for six models, including MA100, EWMA, CCC, BEKK, return-based DCC, and range-based DCC. In the second part, the range-based volatility model is used to examine the economic value of volatility timing in a mean-variance framework. We compare its performance with a return-based dynamic volatility model in both in-sample and out-of-sample volatility timing strategies. For a risk-averse investor, we examine whether the predictable ability captured by the range-based volatility models is economically significant or not. In the last part, we use ranges to estimate the minimum variance hedge ratios within the framework of the CCC model and the DCC model. Other alternative methods used for comparison include the static OLS model, the week-by-week rollover OLS model, the return-based CCC model, and the return-based DCC model. While the spot price risk is hedged by their corresponding futures, we compare the out-of-sample performances of the hedging strategies for the selected commodities, including stock index, currency, metal, grain, soft, and energy markets. Overall, the range-based volatility models perform better than the other selected volatility models in the empirical studies.