# What does it mean with regards to market conditions that the historical volatility is twice the implied volatility

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?

• 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. Commented Sep 19, 2023 at 5:54
• 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 Commented Sep 19, 2023 at 6:11
• thanks for the reference Commented Sep 19, 2023 at 6:13
• 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. Commented Sep 19, 2023 at 8:58
• 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". Commented Sep 19, 2023 at 18:30