1973年，Black-Scholes以熱傳導原理發表了著名的選擇權定價模型，在往後的30多年的時間為近代財務開啟了一條康莊大道。但是，Black-Scholes的基本假設過於簡化現實生活當中可能會面臨到的問題，因此許多新模型皆陸續的誕生，如隨機波動模型、隨機利率模型、跳躍-擴散模型等等。而這些新模型也都是秉持同樣一個理念，也就是進一步修改Black-Scholes模型使其新模型能夠更準確的去計算出選擇權價格。 自從1987年發生了全球股災後，許多學者便針對所謂波動度微笑現象來做研究並加以改善此現象的發生。因此本文主要探討Heston的隨機波動度模型是否在台指選擇權方面也能比Black-Scholes模型之定價誤差來的小；並且加入另外兩種也是以改善Black-Scholes波動度假設的模型，包含了Merton的跳躍-擴散模型以及固定彈性波動度模型(CEV)。實證研究主要去衡量及比較模型價格和市場價格之誤差，並進行顯著性分析及誤差分析。本文的實證結果指出： 1. 樣本內的買權，Merton、Heston隨機波動度或CEV模型皆優於Black-Scholes模型。樣本內的賣權，整體部分以Heston隨機波動度模型為較佳模型。 2. 樣本外買權部分，以CEV模型之預測效果為較佳。另外，Merton模型未有明顯優於Black-Scholes模型。樣本外賣權部分CEV和Heston模型較好。 3. 樣本外誤差分析，主要的影響變數為價性程度以及到期期間，利率在買權部分有較明顯的影響。 This study is mainly to correct one of the Black-Scholes model assumptions. To assume volatility is a constant value which is not appropriate and to correct it. Since the Black-Scholes model occurred the famous volatility smile effect in the 1987’s market crash. My study is to use Merton’s jump-diffusion model, Heston’s stochastic volatility model and CEV model. These three models improved B-S model and to reduce volatility smile; moreover, to predict precisely the option price. Through these three models against BS model, to see whether there is a better improvement in using the TAIEX Options. The methodology is to use Fast Fourier Transform, Fast Fourier Transform no need to assume the underlying follow some distributions. It only needs the characteristic function of the model to calculate the model price and to do error analysis with the market price. The conclusion is that these three models improve the BS model indeed.
