資產報酬分布相對常態分配一直以來存在峰度和偏態的差異，而混和常態模型擁有近似任何連續分配模型的特性，並能夠捕捉峰度、偏態和多模型財務時間資料。統計理論對於估計精準度的評估常常忽略模型選擇的重要性，本文藉由加入選擇權資料來討論模型選擇的問題。由選擇權定價公式可以知道選擇權價格和標的物價格存在特定關係，因此本文探討結合股票報酬資料和選擇權資料進行波動率估計，並利用拔薛法建立信賴區間來評斷估計精準度。我們藉由模擬來檢視聯合估計的表現，另外也將此方法運用在台灣金融市場。

The distribution of returns on financial asset has been found to exhibit substantial leptokurtosis, in many cases, also skewness relative to normal distribution. One attractive property of the Mixture normal model is that it is flexible enough to accommodate various shapes of continuous distributions, and able to capture leptokurtic, skewed and multimodal characteristics of financial time series data. Statistical theory ignores model selection in assessing estimation accuracy. Here we try to add option data to discuss the problem of model selection. Finance theory shows that option prices depend on the underlying stocks’ prices, thus the two kinds of data are related. This paper explores the approach that combines both stock return data and option data to perform the statistical analysis of volatility and consider bootstrap methods for computing confidence interval to illustrate the accuracy between two data sources. A simulation study is conducted to check finite sample performances of the proposed joint estimation. We also have the empirical result in Taiwan finance market.

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