交易量在估計期貨市場動態極端風險值的角色

Role of Trading Volume on the Estimation of Dynamic Extreme Value-at-Risk in Futures Markets

晚近，動態極值理論基礎(dynamic EVT-based)的GARCH族群模型已逐漸成為全球主要金融機構在估計其持有資產部位市場風險值(value-at-risk, VaR)之較為偏好採用之模型。不過再精緻之模型在實際運用上仍有賴於充份之資訊；依混合分配假說(mixture distribution hypothesis)之內涵，交易量(trading volume)具有資訊到達(information arrival)之功能，因此在理論上，金融資產之交易量可能與報酬波動性具有顯著關聯。然而，現行常用之動態極值風險值模型怠於將金融市場由不對稱交易量變動所引發的報酬波動性納入考量。據此，本研究之目的旨在探討將交易量納入動態極值風險值模型架構，是否能改善期貨市場資產風險值估計的精確性。實證分析部份，嘗試採用三種常用不同規格之動態極值理論基礎風險值模型加入交易量(volume, V)進行剖析。其中，包含GARCH、GJR、EGARCH等三組動態極值風險值模型。觀察期間自1997年1月初至2001年12月底，而以NATURAL GAS期貨、NASDAQ INDEX期貨與S&P 500 INDEX期貨等三個期貨資產為樣本，採二階段分析法，首先將交易量納入前述三種常用之動態極值GARCH族群模型估計其風險值；其次，運用回溯測試(back testing)計算穿越次數，並輔以均方差根(RMSE)評估模型的精確性。實證結果，發現有考量交易量之模型精確性均優於傳統動態極值理論法；而在三組模型中，又以GJR為最佳。

The dynamic EVT-based GARCH model has evolved as a preferred approach in the estimation of value-at-risk (VaR), in global financial institutions. Sophisticated risk models also require full information, however, the traditional standard dynamic VaR model failed to account for an important nature of return volatility driven by asymmetric volume changes in the financial markets. The main objective of this study is to investigate whether an incorporation of trading volume improve the accuracy in the estimation of VaR in future markets. Using alternative dynamic EVT-based GARCH family VaR models including GARCH, GJR and EGARCH, over the period from Jan. 1997 to Dec. 2001, the study examine VaRs of three major US futures markets, NASDAQ INDEX, S&P 500 INDEX and NATURAL GAS. Consistent with our a-priori expectation, the finding indicates that the proposed alternative dynamic EVT-based GARCH family VaR models with volumes, in general, outperform traditional dynamic EVT-based VaR models. In particular, GJR+GPD+V is the best model among the others in terms of both rate of violation and RMSE.