選擇權報價異常下波動率指數之計算

Abstract

在日趨複雜金融市場中，投資者對於風險管理的重視程度與日遽增。而波動率指數(VIX)為測度風險的重要指標之一，不僅芝加哥選擇權交易所(CBOE)針對重要的加權股價指數編製波動率指數，世界各國的交易所也紛紛針對其國內的重要加權股價指數編製波動率指數。目前世界各國有編製波動率指數的交易所，其波動率指數皆是從選擇權價格以加權平均方式計算出的。然而各國的交易所仍有許多以各項重要的金融資產為標的的選擇權未被編製成相對的波動率指數。選擇權報價異常為其主要原因之一。但是直接探討選擇權價格是無意義的，需透過已知的市場資訊，找出價格中的內涵資訊－隱含波動率，藉以判斷價格異常與否。本論文提出以統計方法為基礎的演算法，找出異常的隱含波動率並加以修正。之後，再應用於芝加哥選擇權交易所的新波動率指數編製法。以台指選擇權為例，透過本文所提之演算法及相關文獻的佐證，確實能有效的找出異常的報價加以修正。若將此演算應用於發展成熟的市場，還能用於檢測市場對於重大金融消息的異常反應。

In the complicated financial market, investors pay more and more attention to risk management. Volatility index (VIX) is one of the most important indicators of the risk measurement. The volatility index is calculated not only in the Chicago Board Options Exchange (CBOE) but also calculated in the exchanges of the whole world for their important stock index. The volatility index is calculated from the weighted average of option prices. However, many important financial assets which are traded in the option market are not elaborated in the concept of volatility index. One of the main reasons is that these option prices bear irrational quotes. Under condition that market information is known, the volatility implied on option price can be calculated from an option pricing model, which put forth the possible detection of the irrational option price. This thesis proposes a methodology based on statistics to find the irrational implied volatilities and pursue a better modification. The new CBOE VIX can be applied in the calculation of the volatility index. Take the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) for example, we can find the irrational quotes effectively that apply the proposed methodology. Henceforth, our irrational reaction of the important financial information can be successfully detected by our proposed methodology in the mature financial market.