台指選擇權隱含波動指標預測品質之解析

The Forecasting Quality of TXO Implied Volatility Indexes

趙芳靖(Fang Ching Chao)

指導教授 ： 謝文良 ； 李進生

淡江大學/商學院/財務金融學系碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00316

摘要

芝加哥選擇權交易所在1993年推出以著名的Black-Scholes模型為基礎的波動性指標VXO，在2003年更推出新制的波動性指標VIX，而在台灣，自從2001年台指選擇權上市以來，並沒有正式的波動性指標資訊可供投資者參考，為探討台指選擇權波動性指標的預測能力，本文仿照美國CBOE所公佈的波動性指標編製方法，建立兩種不同的台灣隱含波動性指標，再加入歷史波動模型，以RMSE，MAE，MAPE三種誤差分析加上GMM迴歸分析作為檢視波動性模型預測能力績效，比較何種波動度較接近現貨市場的真實波動性。
實證結果發現隱含波動性指標較歷史波動模型更能解釋真實波動性的變動，而以日資料的型態下，舊法所編製的TVXO較新法的TVIX在台指選擇權市場中，更具有配適性。且由於波動性指標和其計算基礎的加權指數呈反向連動，故VIX常被用為判斷市場多空的逆勢指標。另外更進一步探討波動性與報酬率之間的關係，同一時間下，波動性變動與報酬率呈現負相關。然而報酬率在正負不同情況下，對於波動性變動也不同，波動性對報酬率下降的反應相對上漲來的大，顯示出波動性具有不對稱性，在跨期的因果分析中，波動性變動相對報酬率來說是有領先性的，但跨期間的關係不如同期來的明顯。
綜合以上可知，波動性指標可做為未來實際波動率之良好估計值，且又以TVXO具有較高之預測能力，未來仍可持續對兩指標進行研究與分析，並期待台灣發展出自己的波動性指標。

關鍵字

波動性 ； 波動性指標 ； 指數選擇權

並列摘要

In 1993, Chicago Board Options Exchange (CBOE) introduced the volatility index VXO based on the famous Black-Scholes model and CBOE introduced new volatility index VIX in 2003. In Taiwan, however, since TAIEX options have listed in 2001, there is no formal volatility index information available as reference for investors. To research the forecasting ability of volatility index for TAIEX options, we imitate CBOE’s announced editing method to construct two different Taiwan implied volatility index. The indexes plus historical volatility model can be check the forecasting efficiency of volatility models to compare which one’s volatility is closest to the market’s realized volatility by the regression analysis, GMM and three error analyses including RMSE, MAE and MAPE.
The result reveals that implied volatility is better than historical volatility model as to explanation for realized volatility and the TVXO edited by the old method is more adaptive than the TVIX with the daily data in the TAIEX options market by the new method. Besides, because the volatility index makes inverse motion with the based weighted index, the VIX is often considered as the inverse-trend indicator to judge the market’s condition.
To study the relation between volatility and return rate, we find the variation of volatility is negative-correlated with the return rate at the same time point. However, while return rate is positive or negative, the response for variation of volatility is different. The situation that volatility responds more with decline of return rate than with rise of return rate, reveals the volatility having the asymmetry property. In cross-period analysis, compared with return rate, the variation of volatility has the leading property, but the relation in cross-period analysis is not more significant than in the single-period analysis. Conclusively, volatility can be a good estimate for realized volatility and TVXO has better forecasting ability especially. In the future, we will make continuous research and analysis on two indexes and we expect the volatility for Taiwan will be developed.

並列關鍵字

Volatility ； Volatility Index ； Index Option

參考文獻

江木偉 (2003)。台指選擇權隱含波動率指標之資訊內涵—新編VIX指標之實證。台灣大學財務金融研究所碩士論文。

許溪南、詹世煌、謝宗祐 (2000)。選擇權波動性與標的資產歷史波動性及選擇權參數之關聯性。亞太管理評論，5，385-401。

Akgiray, V. (1989). Conditional heteroscedasticity in the series of stock return evidence and forecasts. Journal of Business, 62, 55-80.

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-653.

Bollerslev, T. (1986). A Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327.