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I am trading the Indian market indices. I calculated the last three years historical volatility. Noted down 1 standard deviation of this value.

Then I took a weekly expiry of options on this index and calculated 1 standard deviation by the following formula:

1Sd = index_price*IV*sqrt(7/365)

The option I chose has 7 days to expiry and it’s an OTM Put option with delta 0.1

The historical standard deviation :volatility is almost twice the standard deviation 1Sd calculated above

The question is what does it say about the market? We still have crazy moves intraday but the market has been in an uptrend for the past 4 months, does it mean that options are underpriced?

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    $\begingroup$ I don't think it makes much sense to compute the three year HV and compare it to a very short dated deep ITM put. See here for details. I also am not sure if you computed HV properly, given both IV and HV should be an annualised number. $\endgroup$
    – AKdemy
    Commented Sep 19, 2023 at 5:54
  • $\begingroup$ HV is computed as std_dev of daily returns (today's closing/previous day closing -1)*100, std_dev/HV is just the std_dev for it. HV annual is HV_day*sqrt(365). It's not wrongly calculated, its done is simulation using standard array operators in python. to the first point, if short term volatility is less than historical one, then premium prices should reflect that $\endgroup$ Commented Sep 19, 2023 at 6:11
  • $\begingroup$ thanks for the reference $\endgroup$ Commented Sep 19, 2023 at 6:13
  • $\begingroup$ It is usually log returns (should not be a big difference) and you cannot use 365 because you only observe about 260 or so observations a year. That is one reason why you are a lot higher. The link I gave shows how to replicate Bloomberg's HV tool in Python. That way HV and IV should be directly compared, no multiplication with the index value. $\endgroup$
    – AKdemy
    Commented Sep 19, 2023 at 8:58
  • $\begingroup$ You wrote " the market has been in an uptrend for the past 4 months" that would justify a reduction in IV (the so called "leverage effect of volatility". $\endgroup$
    – nbbo2
    Commented Sep 19, 2023 at 18:30

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Factually, it means that traders are pricing options as if they were less volatile than what actually happened in the past.

It's easy to conclude that this means people generally believe the volatility will be less in the future.

I wouldn't call it underpriced. It would be underpriced if IV was wrong, and there was actually a lot of volatility coming in days ahead. But usually markets are pretty good at predicting volatility, and it's not likely that you will see something they didn't. Meaning that you're unlikely to make profit simply trading on the thesis that IV is too low compared to HV.

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