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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.

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Which options are you testing this with? ATM near-expiry S&P? Or something rather illiquid? –  chrisaycock Jul 31 '12 at 18:39
    
Hello HR. Can you show up you code? This may be easier to understand what's wrong. –  edouard Jan 10 '13 at 21:54
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1 Answer

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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