緩長記憶真實波動性與決定性波動函數在台指選擇權市場的預測能力分析

Forecasting Ability for Long Memory and Deterministic Volitility Function on TXO.

龔志澐(Chih-Yun Kung)

指導教授 ： 段昌文

淡江大學/商學院/財務金融學系碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.00545

摘要

本文驗證台指選擇權在2001年12月到2008年5月間的選擇權價平 (at the money, ATM) 波動率、決定性波動函數 (deterministic volatility function, DVF) 的波動率與 ARFIMA 真實波動率 (realized volatility, RV)，進一步分析包含式迴歸模型對台指選擇權隱含波動率之預測能力，特別地，本文以預測值作為其相依變數。
實證結果顯示，台股現貨指數之波動性不但有緩長記憶 (long memory)，且適用以ARFIMA模型來配適。互相比較三個預測變數之下，預測模型以DVF對全契約的隱含波動率預測能力最佳，此外，同時加入三個波動性預測值之後的包含式迴歸，其對全契約的隱含波動率預測能力最高，樣本外的預測誤差亦為最小。
最後，為了驗證包含式迴歸模型的預測能力，本文須檢視其在台指選擇權市場能否獲利。透過風險中立 (delta neutral) 的選股策略，本文建構跨式 (straddle) 投資組合的交易策略。投資績效顯示，以同時加入ARFIMA真實波動率和決定性波動函數預測值之兩變數包含式迴歸，其一週投資績效為最佳；此外，上述預測誤差最小之包含式迴歸模型，不論在有無考慮交易成本下，皆可獲得正向報酬。

關鍵字

包含式迴歸 ； 緩長記憶 ； ARFIMA ； 真實波動性

並列摘要

The paper estimates the implied volatilities of the at-the-money (ATM) option, deterministic volatility function (DVF) and realized volatility (RV) using ARFIMA model derived from TAIFEX options on Taiwan stock index during December 2001 to May 2008. We compare the predictive ability of encompassing regression model, especially, we use the predicted values as independent variables.
The results indicate that we confirm not only the presence of long memory behavior in the TX volatility but also accurately fitted by ARFIMA. Comparing the different predictive variables, we find the DVF model has the highest forecasting ability of implied volatility for call and put options. Moreover, after including three predictive variables, the encompassing regression has the highest forecasting ability of the implied volatility in the sample and the smallest forecasting error out of the sample for call and put options.
Finally, in order to examine the forecasting ability of the encompassing regression model, we need to tell whether implied volatility forecasts can be used to formulate profitable out-of-sample trading strategies in TXO market or not. By using delta-neutral option, we construct straddle portfolios to estimate benefits of trading strategies. The results show that the encompassing regression with the realized volatility and DVF volatility of one week straddle portfolio has the best performance. Furthermore, regardless of the transaction cost, the encompassing regression with the smallest forecasting error can get positive return in TXO market.

並列關鍵字

encompassing regression ； long memory ； ARFIMA ； realized volatility

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