ARMA-TGARCH 模型之建立

Abstract

ARMA-TGARCH模型是針對GARCH模型探討資產報酬序列之波動群聚性，僅考慮干擾項之大小但未考慮到方向之缺失進行修正，本模型是以干擾項序列前一期當成門檻 (threshold) 變數，且以「0」作為干擾項正、負報酬之分界點，故稱之為TGARCH模型，以補GARCH模型未考慮到方向之缺失。在模型建構方面平均數部份係以ARMA模型建立、誤差項部份則以TGARCH模型配適。本模型可解釋波動性、波動性變動率、隱含波動性均會隨著干擾項變動方向不同而呈現差異的現象，較EGARCH易於處理非對稱性的資產報酬序列，並可將本結果推廣到Black & Scholes (1973) 選擇權定價公式中的風險項，以提升投資決策品質。我們以臺灣、日本及美國證券市場之實際交易資料為例進行ARMA-TGARCH模型之操作示範。

The purpose of an ARMA-TGARCH model is to modify GARCH models assume that only the size and not the positivity or negativity of unanticipated excess returns volatility determines features . In this paper, we use the previous shock of lag-1 act as threshold variable and adopt the 「0」value treat as the branch point of positive and negative shock to build volatility models, hence, it is called a TGARCH model. For building model, the conditional mean term is constructed by an ARMA model and the conditional variance (or volatility) is built by a GARCH model. The result of this model can interpret as follow: (a) Volatility, the change rate of volatility and implied volatility depend on the sign of the former shock.(b)It is more simpler than an EGARCH model for capturing the sign of shock.(c)To extend the result to evaluate risk term of Black & Scholes (1973) options model. The method is used to estimate a model of the risk premium on the Taiwan, Japan valued-weight market index and IBM company stock returns.