To offset this effect, the options need to be reweighted. The result of this reweighting is illustrated in Figure 2. The options demonstrate the same relative sensitivity to implied volatility in the portfolio regardless of the underlying index price.
Figure 2
This is achieved through weighting the options by the inverse of their strike prices, squared. So, options with lower strike prices are given a higher weight to make up for the fact that they naturally have less sensitivity to changes in implied volatility.
This is the essence of the VIX calculation: a reweighting of the options so that exposure to implied volatility rises and falls independently of the underlying index price level. This is what allows VIX to be VIX, a pure measure of volatility, uncontaminated by other effects and factors.
For a deeper dive into this concept – and better charts! – I recommend reading a renowned paper published by Goldman Sachs in 1999. The ideas in this piece served as the foundation for the modernization of the VIX methodology, which took place in 2003.
This article was written by Reid Steadman, managing director, non-equity indices, S&P Dow Jones Indices.
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