The VIX, the CBOE volatility index, is widely used as an indicator of investor fear. High levels of VIX are associated with market turmoils while low levels with calm confident markets. The upward spikes in the VIX usually occur in periods of strongly declining markets. For example, during the market crash of 1997 the VIX exceeded level of 100%. During the financial crisis of 2008, the VIX reached highs of 80%. Market volatility, however, does not result only from the fear in the market but from any new information that disturbs current levels of the S&P 500 index. Therefore, we can observe periods of simultaneous increases in the value of the S&P 500 and the VIX as well.  
The VIX is constructed from at-the-money and out-of-the-money nearby and second-nearby SPX call and put options (\citet{Whaley_2000}\citet{Whaley_2008}). It is widely documented that implied volatility is not constant across different moneyness levels leading to well known volatility smile (figure 1).