透過時間序列以及界外值偵測研究隱含波動度：以金融海嘯之後的臺灣為對象

Abstract

吾人利用臺灣證券市場資料，計算自2008年至2013年之臺灣證券交易所發行量加權股價指數選擇權的隱含波動度，了解此段時間之內，市場結構因為受到「金融海嘯」危機衝擊，無論是在隱含波動度的縱斷面部分（時間序列）還是隱含波動度的橫斷面部分（「波動度的微笑」），其實資料特徵與以往的情況已經產生了十分明顯的不同。我們首先希望利用郭維裕、陳威光、陳鴻隆、林信助（2009）的兩階段動態模型捕捉這些現象，然而發覺他們的兩階段動態模型，對於自2008年至2013年的資料而言，不僅在理論上具有缺陷，而且沒有辦法捕捉極端市場狀況當中特殊事件如何影響隱含波動度的行為。職是之故，我們利用博克斯－詹金斯（Box-Jenkins）的目光來審視郭維裕、陳威光、陳鴻隆、林信助（2009）的兩階段動態模型於隱含波動度縱斷面部分的缺陷，透過匡正模型，改善樣本內的擬合能力以及樣本外的預測能力，並且援引界外值偵測的技術，更有效地讓資料為自己說話，挖掘出埋藏在隱含波動度的資料當中之對於市場歷史衝擊的紀錄。

We use data of Taiwan securities markets to work out a panel data (volatility surface) of implied volatilities of near-month Taiwan Stock Exchange Capitalisation Weighted Stock Index Options from the year of 2008 to the year of 2013, and discover that there have been a structural difference in both the time series and the volatility smile of implied volatilities between pre-financial-tsunami Taiwan and post-financial-tsunami Taiwan. To begin with, we have considered utilising a two-step dynamic model by Kuo et al. (2009) to investigate the panel data, but we advert that there are in fact theoretical blemishes rooted in the longitudinal section of the two-step dynamic model. As a result, we adopt the Box-Jenkins autoregressive integrated moving average model in this work to eliminate the theoretical blemishes and to improve the capability of in-sample fitting and out-of-sample forecasting. Moreover, for the purpose of better capturing the effects of extreme events on the longitudinal data, the tools of outlier detection and adjustment are also been introduced into this work. Our result shows that (1) the two-step dynamic model is really improved so that we can merely rely on implied volatilities themselves to describe the time series in sample without contradict any fundamental assumption of models and to provide much more precise forecast when we want to do price discovery, and that (2) we can quantitatively dig out from transaction records the traces left by and the degree of impact resulted from extreme events.