波動性預測與未來股價預測比較-以臺指選擇權為例

Abstract

一般傳統都以歷史資料為基礎的歷史波動率模型和時間序列模型來估計股 價波動率，本文進一步將選擇權所隱含的資訊形成轉換函數模型納入考量並進行比較分析，檢測各波動率模型的內含資訊及對未來股價真實波動的預測能力。實證顯示，時間序列模型相較於隱含波動率模型提供較多的資訊，然而在不同的誤差衡量指標結果發現，隱含波動率模型中又以價平賣權隱含波動率為最佳波動預測模型。此外，除了歷史波動率模型之外，其他波動率模型在加入成交量資訊後，皆無法提升其模型的預測能力。最後，本文以歷史波動率、時間序列模型波動率和價平買權和賣權隱含波動率等模型評價樣本外價平選擇權。在買權與賣權的評價結果中，買權以時間序列模型計算的波動率評價能力較佳，賣權則是以價平賣權隱含波動率模型表現較佳；然而，整體來看，時間序列模型所隱含的資訊不僅對未來股價波動有較好的預測能力，用以評價未來選擇權的價格也會得到較小的誤差，而除了時間序列模型以外的其他波動率模型，內含資訊較豐富的模型其評價績效也相對較好。

In the past, there were many literatures using the historical model and time series model which are based on historical information or implied volatility model to estimate the volatility of stock price. In this thesis, we use the historical model, time series model, and the transfer function model of implied volatility to forecast the volatility and compare the information content and forecasting ability of these models. From the empirical results, time series model performs better than the transfer function model of implied volatility. Besides, from the results of error analysis, among the transfer function models of implied volatility, the at-the-price put option implied volatility model performs better. Moreover, except for the historical volatility model, all models don’t improve their forecasting ability after adding the trading volume in. At the end, we use these models to price the out-of-sample at-the-price TXO. We find that time series model performs the best in pricing call options, and the transfer function model on implied volatility of at-the-price put option performs the best in pricing put options. However, overall, time series model have better forecasting ability towards the volatility of future stock price and also has smaller error in pricing options.