摘 要 自1973年Black-Scholes提出選擇權定價模型之後,相關文獻對於各種不同條件下選擇權定價模型的研究,也陸續地被探討與推廣,本研究擬採用不同的選擇權定價模型,來檢驗各模型的評價績效。 本文利用歷史波動性、修正後的BS波動性估計方法及無母數核迴歸之波動性估計方法搭配BS模型,以及GARCH選擇權定價模型下之解析近似值等方法,觀察並試算同一契約的選擇權理論價格,並比較其與實際市場價格間的差異情形,以探討各模式的績效及適用性。 本文以台灣加權股價指數選擇權(TXO)進行實證分析,並以平均絕對誤差(mean absolute error, MAE)、平均誤差百分比(mean percentage error, MPE)及箱形圖(box plot)、均方根誤差(root mean squared error, RMSE),做為價格誤差的衡量指標。並且以勝率比(wins)來衡量何種估計方式及模型下,所計算而得之理論價格接近市場價格的次數較多,做為相對績效衡量的依據。並對市場價格與理論價格不一致的原因進行差異分析,以距到期日時間、成交量、涉價比、標的資產波動性、報酬率、偏態係數、及峰態係數等七項因素對模型偏離市價程度進行多元迴歸分析。 實證分析結果可知,傾向使用較簡單的模型及波動性估計方式,過去對台灣選擇權市場所進行之相關實證文獻結果一般而言,顯示沒有足夠證據可證明隨機波動性模型績效優於傳統BS模型,本文實證結果強化了此一推論。
Abstract Since Black and Scholes published the option pricing model in 1973, a lot of studies have tried to investigate option pricing model under different conditions. This research try to test the performances of different option pricing model. This study uses historical volatility, ad hoc volatility estimation and nonparametric kernel regression volatility estimation with BS model, and the analytical approximation of GARCH option pricing model to calculate the theoretical option price. The best model is determined by comparing the market prices. We analyze TAIEX Options (TXO) and use mean absolute error(MAE), mean percentage error(MPE), box plot and root mean squared error(RMSE) to be the measured indicator. And we use Wins to measure what methods can get the theoretical price closer to market price than other models. Finally, we use the time to maturity, transaction amount, moneyness, volatility of underlying assets, rate of return, skewness, and kurtosis to run the multi-regression, to analyze the pricing error. The empirical results indicate that we tend to use simple model and volatility estimation method. For the past TAIEX Option market, some empirical results reveal that the performance of BS model outperform the stochastic volatility model.