Why Historical Volatility Above Implied Volatility Does Not Prove Options Are Cheap

Summary

The document compares an estimate of historical volatility from three years of index returns with the volatility implied by a one-week, out-of-the-money put on an Indian market index. The question describes historical standard deviation as roughly twice the option-based one-standard-deviation move, calculated using index level, implied volatility, and time to expiry. The market had also been trending upward despite sharp intraday moves, prompting the question of whether options were underpriced.

The response says the comparison means option prices reflect lower expected volatility than the amount realized over the chosen historical sample. That difference alone does not establish mispricing: historical volatility describes the past, while implied volatility reflects market pricing for the future. Options would be underpriced only if future volatility exceeded what is priced in. The answer cautions that a trader is unlikely to earn a profit simply from observing that implied volatility is below historical volatility. It offers no forecast, statistical test, or evidence that the implied estimate will prove wrong, and the historical window may not represent the option's short horizon.

Key ideas

• Historical volatility measures realized past movement, while implied volatility reflects option market pricing for future movement.
• A gap between the two does not by itself show that options are mispriced.
• Options are underpriced only if subsequent volatility exceeds what their prices imply.
• A historical comparison alone does not establish a profitable volatility trade.

Tags

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


# 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?

## Answer by gomennathan (score 1)

https://quant.stackexchange.com/a/76732

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.