台指選擇權在Black and Scholes模型中最佳波動性估計

The Method of the Optimal Volatility Estimator In Taiwan Index Options Market under Black and Scholes Model

黎仁鈞(Jen-Chun-Li)

指導教授 ： 倪衍森

淡江大學/管理學院/管理科學研究所碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00960

摘要

台灣證券期貨交易所自從2001年初發行台灣指數選擇權以來，建議以Black and Scholes模型作為選擇權評價的工具，模型中包含五個變數，分別為標的資產價格、履約價格、無風險利率、到期期間與波動性。其中波動性的取得相當不易，本研究主要目的在於波動性估計的設計與探討台灣指數選擇權的價格誤差及最適估計。

研究期間採用2004/7/1至2004/12/31上午九點至下午一點三十分台灣指數選擇權日內每十五分鐘資料。並且設計四大類型波動性，分別為歷史波動性、GARCH波動性、隱含波動性及GAIV，共二十種估計方法。套入Black and Scholes模型後，取得理論價格，並與市場價格做比對，運用MAE、MAPE、統計T檢定與迴歸分析方法進行判別何者為最適波動性估計。

研究中發現，不論買賣權別皆以Vega風險係數為權數估計的隱含波動性為最適估計，可以使價格誤差降至最低，而以時間序列模型為估計的波動性效果顯著不佳，尤其以歷史波動性為最差；而GARCH波動性透過GAIV的結合可以明顯的修正其效果。

關鍵字

台灣指數選擇權 ； Black and Scholes模型 ； GARCH ； 隱含波動性 ； Vega風險係數 ； 時間序列模型

並列摘要

Taiwan Futures Exchange has distributed the Taiwan Index Option since 2001, suggested that took the option appraisal tool by Black and Scholes Model. In the model contains five variables, respectively be the Underlying Asset price, Exercise Price, Risklss rate of interest, the Period of Maturity and Volatility. It is not easy thing to predict the volatility precisely. The purpose of this research is to find a suitable estimation method to evaluate the price of Taiwan Index Options and find out which estimator is the best.

By using intra data of Taiwan Index Options that are collected from morning 9:00 to 1:30 pm between 07/01/2004 to 12/31/2004 as our sample. In this research, we design four types of volatilities including twenty methods. Four types are History Volatility, Garch Volatility, Implied Volatility and GAIV. The estimated values generated from the models were then bring into the Black and Scholes Model and to evaluate the difference between market price and theory market price with a target to find the optimal volatility measure method.

The result we find out whether the options are Calls or Puts VGIV is the best estimator which makes least price errors. The effect of the estimator of Time Series Model is general not good, especially History Volatility. And GAIV can improves the effect of GARCH Volatility which makes the theory market price aloof from the market price.

並列關鍵字

Taiwan Index Options ； intra Data ； Black and Scholes Model ； GARCH ； Implied Volatility

參考文獻

9、賈景宇，台灣創新型認購權證在不同波動性模型下之比較，中原大學企業管理研究所碩士論文，2001年6月。

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