隱含波動度偏誤之成因探討

Abstract

在實務上，人們習慣拿從選擇權價格中推估出的隱含波動度來當作標的未來報酬波動的估計值，但在過去的研究中，發現不論是由Black-Sholes模型導出的隱含波動度或是由Britten-Jones and Neuberger (2000)導出的model-free隱含波動度當作估計值，兩者皆為不效率且為偏誤的。在本研究中，我們想要探討造成隱含波動度偏誤的原因為何。從過去文獻中，我們找到各種可能相關的因子，包括市場動能（Market Momentum）、市場流動性、市場情緒（Market Sentiment）、週一效應、週五效應、交易成本、市場價格的不連續性（Market Jump），並將這些因子放入模型中檢驗其影響。我們的結果發現所有的因子皆為顯著，表示他們均會造成隱含波動度的偏誤。此外，為了探討市場崩盤前後的影響因子是否不同，我們將樣本依時間拆開成兩個子樣本並分別檢測。我們發現，所有的因子在前後兩期皆為顯著，除了市場情緒因子只有在市場崩盤後的樣本中顯著。這個結果可能是因為在崩盤的市場中，投資人較為敏感且情緒化，所以選擇權的價格容易受到投資人的情緒影響，不能表達其真實價格，所以由選擇權價格導出的隱含波動度也因此產生偏誤。

In practice, people used to use implied volatility to estimate the future volatility. However, the previous studies find both Black-Sholes implied volatility and model-free implied volatility are biased and inefficient. The purpose of this paper is to investigate the determinants of implied volatility bias. From previous studies, we summarize the probable factors, including market momentum, market liquidity, market sentiment, market jump, and transaction cost. Then we test them into our time-series regression model. The result shows that all the factors are robust. In addition, we want to figure out the effect of market crash, so we separate our data into two subsamples and test them respectively. The result is similar to the full sample result, except the market sentiment factor is only significant in post-market-crash sample. Because investors are more sensitive in the bearish market, they buy more put options and the net put buying pressure affect the shape of implied volatility, hence the bias is generated.