Implied Volatility, VIX Construction, and Its Market Relationship
Summary
The document asks how data providers derive implied volatility, what it means to aggregate out-of-the-money option prices in the VIX calculation, and why volatility often rises during falling markets. It points readers to an external explanation of the VIX methodology but does not lay out the calculation mathematically. The answer offers an intuitive risk-and-pricing argument: if investors demand a higher expected return for greater perceived risk, a stock's discounted value falls, putting downward pressure on its price.
The example illustrates this logic with a stock expected to be worth more in a year, then reprices it after the assumed risk and required return increase. The explanation is a simplified account rather than a full model of volatility pricing or market behavior. It does not establish that volatility causes declines, explain leverage or volatility risk premiums, or distinguish the VIX's option-derived expected volatility measure from historical volatility. The question about the sign of historical returns is raised but not directly resolved.
Key ideas
- The VIX uses prices of SPX options across a range of strikes to estimate expected volatility.
- The document refers readers elsewhere for an intuitive explanation of the VIX formula.
- Its proposed explanation links higher perceived risk to higher required returns and lower present stock prices.
- The pricing example is illustrative and does not establish a universal causal relationship between volatility and falling markets.
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Full text
# How is implied volatility derived? # How is implied volatility derived? How to compute Implied Volatility Calculation? The above link shows that there multiple ways to calculate implied volatility. My question is that for most of the common data sources like Bloomberg, Fidelity, etc, how is the implied volatility calculated? https://www.cboe.com/micro/vix/vixwhite.pdf shows that for the VIX index, it "estimates expected volatility by averaging the weighted prices of SPX puts and calls over a wide range of strike prices". What does this mean mathematically? Can anyone shed more light on this? Why is implied vol (and for that matter historical vol) correlated with bear markets and inversely correlated with bull markets? Since historical vol is the standard deviation of historical returns, why should the sign matter? Ie. if I add a point to a dataset that is far from the mean, it will increase variance regardless of the sign. ## Answer by Neeraj (score 8) https://quant.stackexchange.com/a/19201 For How VIX works you can read this wonderful blog : http://onlyvix.blogspot.com/2011/09/intuitive-understanding-of-vix-formula.html It provide wonderful non mathematical explanation of the how vix is actually computed. Now comes to your last answer why vix is inversely related to market movement ? In simple words, if market is more volatile then investor would expect higher return from the market. To get the higher return, traders will continue to sell the stock until its price is consistent with the perceived risk. Lets take simple example : if current price of stock is $ 100 and investor expect price to be 110 after one year. Here expected return is 10 percent which is consistent with the perceived risk of lets say 20%. If this risk increased then investor would expect higher return from the same stock. Assume, risk increased to 25% and investor expect now 12% return. So now the fair price is 110/1.12 = 98.21. So stock is overprice and investor continue to sell it until price reaches 98.21 which is consistent with revised expected return of 12%. Reverse happen when volatility fall. The above explanation is simply based on risk return theory of stock price. I hope it would help you to understand why VIX is inversely related to market movement.
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