Interpreting Implied Volatility as an Annualized Return Dispersion

Summary

The document explains that an option’s implied volatility is an annualized measure of the underlying asset’s return variability inferred from option prices under a pricing framework such as Black–Scholes. A quoted value such as 40% refers to an annualized standard deviation of returns over the option’s relevant horizon; it does not mean the stock is expected to move by that percentage in a day or that the option price itself will change by that amount.

One answer frames the measure using log returns and describes it as the dispersion implied by traded option prices. Another interprets it as a one-standard-deviation range, illustrating the idea with a stock price and a one-year option. The range is a statistical scale, not a guaranteed boundary or a directional forecast. The explanation is simplified: implied volatility depends on the option’s maturity and pricing assumptions, and a single figure does not capture the full distribution of possible returns or specify whether the underlying will rise or fall.

Key ideas

• Implied volatility is annualized and describes return dispersion inferred from option prices.
• A volatility quote does not predict a directional move or describe the percentage change in the option price.
• The one-standard-deviation interpretation scales with the underlying price and the option’s time horizon.
• Implied volatility depends on the option contract and pricing framework, so it is not a guarantee of realized movement.

Tags

# What is IV % actually measuring?


# What is IV % actually measuring?












If the Implied IV of an option is 40%, what is the 40% representing, 40% of what?

Does that mean the underlying stock is estimated it may move up or down 40% in a day, month year?

The option price may move up/down 40%?

Its just an arbitrary number relative to other securities IV %?

## Answer by AlRacoon (score 1)

https://quant.stackexchange.com/a/59898

Implied volatility is the annualized standard deviation of the "lognormal return" of the underlying stock, implied by exchange traded options prices (utilizing the black scholes framework to price the option) for the time period of the expiration of the option.

So if you had a 40% implied vol for 1Yr IBM call options, the price of the call options are implying that if you took the daily log returns of IBM stock for a year, the standard deviation of those returns is 40%. Volatility is annualized.

## Answer by Paul Brennan (score 0)

https://quant.stackexchange.com/a/59897

IV or implied volatility, when represented as a percentage, indicates the annualized expected one standard deviation range for the stock based on the option prices. For example, an IV of 40% on a \$200 stock would represent a one standard deviation range of \$80 over the next year.

When thinking of options as an insurance contract, the more risky it is means that the cost of insuring that risk becomes more expesive.

Basically its a way to compared the cost of the option from stock to stock without having to analyze the underlying cost of the option.

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