Volatility Index Case Study
In 1993, the Chicago Board Options Exchange introduced the CBOE Volatility Index (VIX) which measured the 30-day implied volatility from at-the-money options of the S&P 100. In 2003 CBOE and Goldman Sachs updated the VIX. Now the new VIX is based on the S&P 500 index and estimates the expected volatility by averaging the weighted prices of S&P 500 puts and calls over a large range of strike prices and at two nearby maturities. CBOE used this methodology and back-calculated the VIX since 1990 using historical options price. The CBOE Dow Jones Industrial Average volatility index (VXD) and CBOE Nasdaq-100 volatility index (VXN) were introduced at 1997 and 2001 respectively. The method to calculate the VXD and VXN is identical as the method used …show more content…
The fact that these two different methods of measuring the future realized volatility are similar is very important. Firstly, because it shown that the fair value of variance and the implied squared volatility are equivalent concepts and the implied volatility is a concept very familiar in the literature. Secondly, it explains why the VIX, except that it can be seen as the variance swap rate (squared VIX), it known as the ‘investors’ fear gauge”. The proof on why the equation (1.13) is equivalent with the equation (1.12) is provided in the Appendix B. As explained above the CBOE calculate the squared VIX using the equation (1.8) which is the discretization of the equation (1.12). In line with Jiang and Tian (2007), we discuss the approximations and the problems which occur from the CBOE formula. The equation (1.12) from Demeterfi et al. (1999) it assumes that there are strike prices (K) from 0 to infinity, something which of course it doesn’t stand in the real world. Thus, the CBOE approximate the K=0 with the lower strike price (KL) and the infinity with the higher strike price KH. So, the sum of the two integrals from zero to infinity
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