Model-Free隱含波動度價差之遠期資訊

Forward Information from Model-Free Implied Volatility Spread

黃崇銓(Chung-chuan Huang)

指導教授 ： 王耀輝 ； 葉錦徽

國立中央大學/管理學院/財務金融學系/碩士(2008年)

摘要

本文藉由S＆P 500指數選擇權契約價格，各自計算出買權Model-Free隱含波動度與賣權Model-Free隱含波動度，並且定義出Model-Free隱含波動度價差(Model-Free Implied Volatility Spread)。隨後利用波動度價差的數值，幫助我們探討其價格發現的能力，亦即波動度價差對於未來市場報酬，與未來市場波動度的關聯性。藉由將波動度價差分組，我們發現在極端波動度價差的分組下，在未來皆能獲得顯著異於零的報酬，且皆遠高於市場平均日報酬數倍之多。此外我們還發現波動度價差與未來波動度變化的反向關係。最後在不對稱的波動關係下，低波動度價差分組在未來所面臨的波動風險反而高於高波動度價差分組。顯示投資人若同時考量投資報酬與投資風險，高波動度價差分組較具投資的吸引力。因此本文發現Model-Free隱含波動度價差所涵之遠期資訊，不僅具有價格發現的功能，同時具有輔助波動風險控管的能力。

關鍵字

遠期資訊 ； 價格發現 ； Black-Scholes隱含波動度 ； Model-Free隱含波動度 ； Black-Scholes隱含波動度價差 ； Model-Free隱含波動度價差

並列摘要

In this article, we use the contract prices of S&P 500 index option to calculate the model-free implied volatility of call and put respectively, and define the Model-Free Implied Volatility Spread, MFIVS. We then explore MFIVS’s ability in the price discovery of the underlying, namely the relationships between MFIVS and future market returns as well as its future volatility. After grouping and sorting the volatility spread, we find taking advantage of the information from the extreme groups will have significant higher return than the average market return in the future. Besides, we also find that there is a negative relationship between volatility spread and the change of future volatility. Given the asymmetric impact of volatility spread to future volatility, the group of low volatility spread will face higher volatility risk than the higher ones, which implies that investing in the group of high volatility spread will end up with higher return while at lower risk. To sum up, we find that the forward information embeds in MFIVS is relevant in both the pricing discovery and volatility risk management.

並列關鍵字

Forward Information ； Price Discovery ； Black-Scholes Implied Volatility ； Model-Free Implied Volatility ； Black-Scholes Implied Volatility Spread ； Model-Free Implied Volatility Spread

參考文獻

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