Why Implied Volatility Does Not Exceed Realized Volatility at Every Strike
Summary
The discussion challenges the idea that implied volatility is generally above realized volatility at every option strike. It distinguishes a single strike's implied volatility from an aggregate measure: a variance swap strike combines information across strikes using specific weights, and its difference from subsequent realized variance is the variance risk premium. That premium can be positive or negative, so even the weighted comparison is not guaranteed to favor implied volatility.
The answers also note that realized volatility is most directly comparable with at-the-money implied volatility under standard definitions. Comparing it with out-of-the-money options involves skewness and tail behavior as well as variance, and option prices can reflect direction and sentiment. A premium for bearing option risk may explain why implied volatility often exceeds subsequent realized volatility, while sharp market moves can reverse that pattern. These are conceptual observations rather than a statistical study: no sample, measurement convention, or evidence establishes how often the relationship holds across markets or maturities.
Key ideas
- Implied volatility need not exceed realized volatility at every strike.
- A variance swap strike uses a weighted set of option prices, and its risk premium may have either sign.
- Standard realized volatility is most directly comparable with at-the-money implied volatility.
- Out-of-the-money option comparisons also reflect skewness and tail risk.
- The discussion offers intuition but no empirical test across defined markets or periods.
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Full text
# Implied volatility greater than realized volatility at all strikes? # Implied volatility greater than realized volatility at all strikes? It is usually stated that the implied volatility is statistically generally --- not always --- greater than the realized volatility. It seems this statement is made with regard to the implied volatility at the money or when the strike is equal to the future of the underlying. Is this statement statistically generally true for all strikes? ## Answer by Frido (score 1) https://quant.stackexchange.com/a/81624 A bit late to the party, but no in general it's not true that implied volatility for all strikes is greater than realized volatility. What may be true, but certainly not always true, is that the weighted average of implied volatilities is less than realized volatility. The weights are the weights that give the variance swap strike, and the difference between the variance swap strike today and future realized variance is the variance/volatility risk premium, which can be positive or negative. ## Answer by THATS MY QUANT MY QUANTITATIVE (score 0) https://quant.stackexchange.com/a/77319 Most of the time, but not always. When a trader underwrites an option (selling a call or put), they do not get the choice to exercise - the buyer has the choice. So the buyer pays a "premium" for that choice, similar to the idea of insurance. If you later sold the option and it turns out that the realised vol < implied vol of the contract you bought, then you would lose money. Thus, in the long-run, you lose money when realised < implied vol. It then follows, if one assumes that realised vol < implied vol is always true, like your question, why ever be long options if you always make money being short? Because it's not always true. During black-swan events, realised vol > implied vol. If you look at the VIX, during times when vol is > 40%, traders who are short options are generally selling their options priced at implied vol << realised vol and more often than not, would be losing money. I go back to the insurance analogue. The insurance buyer (long) "wins" during low probability events, but is losing on a day-to-day basis. The insurance seller (shorter) "wins" small amounts on a day-to-day basis ## Answer by Dhruv Mahajan (score 0) https://quant.stackexchange.com/a/77591 Standard realized volatility calculation only corresponds theoretically to ATM strikes not OTMs. Unless you have a different definition of realized volatility you cannot compare it to OTM implied. However, on the whole vol curve level I believe the statement to be true. For a pure ROC analysis you'll generally make more money shorting OTMs than ATMs. The difference starts to occur when you look at the 3rd order and 4th order moments instead of just variance (i.e. skewness and kurtosis). That will be much higher for a short OTM position than a short ATM one. ## Answer by user67825 (score 0) https://quant.stackexchange.com/a/77765 if you look at v short dated SOFR options - at the moment, realised far outweighs implieds. the reason is, implieds are also v directional and sentimentally driven.
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