On the non-linear relationship between VIX and realized SP500 volatility

VIX, a ticker symbol for Volatility Index, measures the implied annual volatility of at-the-money SP500 Index Options. Conventional wisdom presumes VIX to measure the magnitude (positive or negative) of possible movements in future equity prices, with movements being a positive function of VIX. This research investigates the nature of the relationship between VIX and SP500 volatility, and answers the question as to whether that relationship is linear or nonlinear. Based on this research paper, the authors conclude that the realized SP500 volatility is nonlinear, and grows with the level of VIX at an increasing rate. The nonlinearity relationship between VIX and SP500 has enormous implications for investment management and hedging in the financial markets