Estimating Volatility for Option Models Without Implied Volatility

Summary

The document asks how to estimate the volatility input for option pricing when the option's market price, and therefore its implied volatility, is unavailable. One reply presents the usual sample standard deviation of returns as a linear unbiased estimator under its stated framing, and suggests GARCH as an alternative that can capture changing volatility. It also mentions filtering outliers before estimating volatility, though it gives no specific procedure for doing so.

A second reply argues that Black–Scholes-style pricing still needs a volatility estimate, but provides little detail and includes an unclear reference to order books, geometric shapes, and volume. The discussion offers no head-to-head results, data requirements, forecast horizon, or conditions under which GARCH improves on historical estimates. Its useful takeaway is limited: historical return variation and conditional volatility models are possible inputs when implied volatility cannot be observed, but the appropriate choice depends on the application and requires further evaluation.

Key ideas

• Historical returns can be used to estimate the volatility input when option prices are unavailable.
• A GARCH model is suggested as a way to estimate volatility from historical data.
• Filtering outliers is mentioned as a possible preprocessing step, without a defined method.
• The replies do not provide comparative evidence or specify when one estimator is preferable.

Tags

# Is there a better way to price options than with historical volatility?


# Is there a better way to price options than with historical volatility?












I know that annualized historical volatility calculated with closing prices is a much rougher estimate than implied volatility for the correct "volatility" parameter in options pricing models. However, implied volatility requires knowing the market price of the option in question, which is not feasible for my application. Is there a widely used better estimate for the volatility parameter than annualized historical volatility? Thanks.

## Answer by emcor (score 3)

https://quant.stackexchange.com/a/15387

If you want to estimate volatility from historical data, the only best linear unbiased estimator (BLUE) is $$\sigma=\sqrt{\frac{1}{T-1}\sum_{i=1}^T (r_i-E(r_i))^2}$$ Any other estimator will hence either be biased or not consistent.

Another approach could be to estimate volatility via a GARCH model, which has shown good empirical results in the past.

It is also possible to transform the sample data before estimation, i.e. filter for outliers and such.

## Answer by user151781 (score 3)

https://quant.stackexchange.com/a/15389

All option pricing formulas except this one and this one use some sort of historical volatility . I can't see how you can use the Black Sholes framework and not use some sort of historical volatility

- uses an order book

- uses geometric shapes and volume

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.