隱含波動率之模型及預測：以台灣市場為例

鄒紹輝(SHAO-HUI TSOU)

指導教授 ： 鄭光甫

國立中央大學/理學院/統計研究所/碩士(2006年)

摘要

摘要
波動性的問題一直是多年以來各界所著墨的焦點，為了解何種波動性模型所算出的理論價格最貼近於市價，於是本研究利用不同之四種方法，來預測TXO未來一星期的波動度，代入到B-S 模型中得出TXO之理論價格，且利用三種價格誤差的指標，平均絕對誤差(mean absolute errors, MAE)、平均絕對誤差百分比(mean absolute percentage errors, MAPE)及均方誤 (root mean squared errors, RMSE)，來比較理論價格與TXO市場價格的差異，並探討模型、參數及預測能力是否會隨著資料的變動而有所改變。最後再使用成對樣本T檢定，比較不同波動度模型下，所有預測之理論價格與市場價格的價格誤差之差異，是否會有相對顯著，希望藉此能找出一適合的模型，可較準確地預測出TXO的合理價格，以降低交易上的損失。

關鍵字

隱含波動性 ； Black-Scholes 模型 ； GARCH模型

並列摘要

Abstract
The problem of the volatility has been the focus of research for many years. In order to understand the volatility model most suitable for real market data ,we utilize four different models to model the implied volatility for one week TXO future. Three different measurements are used to compare the performance of the models. They are : mean absolute errors (MAE), mean absolute percentage errors (MAPE) and root mean squared errors (RMSE). Real data were applied to study the usefulness of the models.

並列關鍵字

Black-Scholes Model ； GARCH Model ； Implied Volatility

參考文獻

Akgiray, V., (1989), “Conditional Heteroscedasticity in the Series of Stock Return Evidence and Forecasts”, Journal of Business, 62, pp.55-80.

Bollerslev, T., (1986), “Generalized autoregressive conditional hete- roscedasticity”, Journal of Econometric’s, April, Vol 31, pp.307-327.

Box, G. E. P., Pierce, D. A., (1970), “Distribution of residual auto- correlations in autoregressive integrated moving average time series models”, Journal of the American Statistical Association, 65, pp.1509-1526.

Chu, S. H. and Freund, S., (1996), “Volatility Estimation for Stock Index Options: A GARCH Approach”, Quarterly Review of Economics and Finance, 36, pp.431-450.

Engle, R. F., (1982), “Autoregressive conditional heteroscedasticity with estimates of the variance of untied kingdom inflation”, Econometrica, July, pp.987-1007.