Why Implied Volatility Can Exceed Historical Volatility
Summary
The document asks why QuantLib option implied volatilities are consistently higher than annualized historical volatility estimates. Its answer offers an insurance analogy: put options can protect against losses, so buyers pay a premium for that protection. It suggests option writers may price options above the volatility seen in past returns to compensate for taking on that risk.
The explanation is qualitative and does not analyze the sample calculations, option inputs, or how implied volatility is solved from market prices. It also presents a simplified account: implied volatility is a market-derived estimate reflecting option prices and expectations, and its relationship to realized historical volatility can vary. The quoted figures alone do not establish that the calculation is correct or that a volatility premium explains the gap; checking conventions, market data, and contract details would be necessary.
Key ideas
- Implied volatility is inferred from option prices, while historical volatility is calculated from past returns.
- The answer uses insurance pricing to explain why option premiums may reflect a volatility premium.
- A difference between implied and historical volatility is not, by itself, proof of a calculation error.
- The document does not diagnose the sample figures or verify the QuantLib inputs.
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# Interpreting QuantLlib implied volatility numbers # Interpreting QuantLlib implied volatility numbers I am using QuantLib to calculate implied volatilities. I am trying to understand the calculated figures (especially, when compared to historical volatility). The calculated implied volatility numbers are seldom below 0.5, whilst the historic volatility numbers* is never above 0.5. Here is an output from my program: ``` DEBUG: 20 day historic volatility: 0.10 DEBUG: 20 day implied vol: 0.519485358338 DEBUG: 30 day historic volatility: 0.10 DEBUG: 30 day implied vol: 0.515820883886 DEBUG: 40 day historic volatility: 0.12 DEBUG: 40 day implied vol: 0.624451849413 DEBUG: 50 day historic volatility: 0.16 DEBUG: 50 day implied vol: 0.692403434852 DEBUG: 60 day historic volatility: 0.30 DEBUG: 60 day implied vol: 0.492372372425 DEBUG: 70 day historic volatility: 0.27 DEBUG: 70 day implied vol: 0.544712487074 DEBUG: 80 day historic volatility: 0.31 DEBUG: 80 day implied vol: 0.579945073422 DEBUG: 90 day historic volatility: 0.12 DEBUG: 90 day implied vol: 0.489174212819 DEBUG: 100 day historic volatility: 0.31 DEBUG: 100 day implied vol: 0.563068062254 DEBUG: 110 day historic volatility: 0.24 DEBUG: 110 day implied vol: 0.608231639138 DEBUG: 120 day historic volatility: 0.38 DEBUG: 120 day implied vol: 0.62748262992 ``` Can anyone explain why the ivol figures are generally, several multiples higher than the historic vol figures? *Note: Historic vols shown are annualized and calculated as the square root of the variance of log returns. ## Answer by unclepaul84 (score 2) https://quant.stackexchange.com/a/3876 What you are observing is a natural occurence in the options market. If you think of PUT options as insurance, the premium is based on what the historical volatility of the underlying is. If option writers sold you the options at or below historical volatility they on average would loose money. So therefore, they "mark up" the historical volatility and that is how they make the money. HTH
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