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

  • Received March 17, 2017;
    Accepted June 1, 2017;
    Published July 17, 2017
  • Author(s)
  • DOI
    http://dx.doi.org/10.21511/imfi.14(2-1).2017.05
  • Article Info
    Volume 14 2017, Issue #2 (cont. 1), pp. 200-206
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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.

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    • Figure 1. Daily SP Return
    • Figure 2. Dailly Sequence SP500 Return
    • Figure 3. Daily VIX
    • Figure 4. Dailly Sequence VIX
    • Figure 5. Dailly SP500 Return v VIX
    • Figure 6. Dailly Fabdolute SP500 Return v VIX
    • Figure 7. SPR Bin Std. dev v. Mean Bin VIX Outlier Included
    • Figure 8. SPR Bin Std. dev v. Mean Bin VIX Outlier Omitted
    • Figure 9. Residuals v VIX (t-1) – Linear
    • Figure 10. Residuals v VIX (t-1) – Non-linear
    • Table 1. Descriptive statistics – daily SP 500 returns and VIX
    • Table 2. Descriptive statistics By VIX group mean – daily
    • Table 3. Linear regression results of stdev(SPR) = f(VIXt-1)
    • Table 4. Nonlinear regression results of stdev(SPR) = f(VIXt-1 , VIXt-12)