Kernal Smoothed VIX

Abstract:

With the original debut of stock market that can be traced to as early as 12-th century, companies started to use stocks to raise money.  In order to see the trend of the stock market in general, stock market indexes such as S & P 500 were introduced.  Define volatility as the square root of the variance of the price change.  The larger the volatility, the higher the possible profit.  The Chicago Board Options Exchange, together with Goldman Saches, developed a model free method to estimate the expected volatility index, VIX.  The final adapted estimator is the weighted sum of the S & P 500 put prices and call prices over a wide range of strike prices.  To reduce the estimation bias, we explore the possible sources and we believe option pricing errors add more bias to the VIX pricing.  In our paper, we suggest adding a kernel smooth step into the VIX estimation procedure.  Both theoretical and simulation results support our assumption that the estimation bias will be reduced under our targeted cases when kernel smooth is introduced.