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Why Realized and Implied Volatility Need Statistical Calibration

Article Quant Q&A · Author: Bryan Lwy
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Summary

The exchange considers a proposed options signal that buys when forecast realized volatility exceeds current implied volatility. It cautions that this raw comparison is not automatically a valid trading rule because implied volatility often includes a premium over subsequent realized volatility, in part as compensation to option writers for bearing risk. That average relationship makes a simple greater-than threshold questionable.

Instead, the answer recommends first establishing a statistical relationship between realized-volatility forecasts and implied volatility, then using that relationship to design a signal. It also raises a useful check on intuition: even if expected realized volatility exceeds the volatility level at which a delta-hedged call was purchased, profitability is not assured. The document does not specify a calibration method, account for option sensitivities beyond delta hedging, or provide a backtest. It frames these as necessary considerations rather than presenting a tested strategy.

Key ideas

  • Implied volatility may exceed subsequent realized volatility because option sellers demand compensation for risk.
  • A raw rule comparing forecast realized volatility with implied volatility may not be meaningful.
  • A trading signal requires a statistical relationship between the forecast and the option market’s implied volatility.
  • Higher expected realized volatility alone does not guarantee profit on a delta-hedged option position.

Tags

OptionsVolatilityDerivatives pricingBacktesting
Full text
# Realized volatility forecast vs Implied volatility


# Realized volatility forecast vs Implied volatility












I have forecasts of realized volatility, as well as implied volatility for individual traded options of the S&P500.

I want to simulate a simple trading strategy; that is, buy signal=1 if forecasted realized volatility is greater than current implied volatility. However, the literature documents that implied volatility is usually higher than realized volatility.

Are there any better approach for this simulation?

## Answer by Ezy (score 5)

https://quant.stackexchange.com/a/42584

On average the implied volatility is higher than realized volatility because you can easily imagine that dealers will ask customers to pay a premium to write them options and risk manage them

you can have a look at this paper for instance

PIMCO-The Volatility Risk Premium

Now you can investigate how realized volatility can be a signal for trading implied vol but the condition will certainly not be "buy when realized > implied" because the 2 quantities are not directly comparable. You need to establish some statistical relationship first.

And to finish here is a little exercise to test your thinking about realized vs implied vol and hopefully help you design properly your strategy: suppose you are long a call option which you purchased at some implied vol level $\sigma_0$ and which you are delta-hedging. Now imagine that i grant you that "on average" over a period of time the stock realized volatility $\sigma_r$ will be higher than $\sigma_0$. In other words i tell you that in expectation $$E[\sigma_r] > \sigma_0$$

Would you be certain to make money even in this situation ?

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.