Realized vs Implied Volatility - The Gap That Drives Volatility Trading

By EC Assets Research Team, Volatility Research · Published 20 May 2026 · Updated 15 October 2026

Realized vs Implied Volatility: Realized volatility measures how much an asset has actually moved, computed from past returns; implied volatility measures how much the options market expects it to move, backed out of option prices. The persistent gap between them - implied usually exceeding realized - is the variance risk premium that underpins most volatility strategies.

Two Volatilities Looking in Opposite Directions

Volatility comes in two forms that are often confused. Realised volatility, also called historical volatility, measures how much an asset has moved, computed from past returns. Implied volatility measures how much movement the options market is pricing, backed out of current option prices. One looks backward at what happened; the other looks forward at what is paid for.

The two are linked by trading. A delta-hedged option holder earns money when the asset moves more than the option's implied volatility assumed and loses when it moves less. That makes the gap between implied and subsequently realised volatility the central quantity in volatility trading.

How It Works

Realised volatility. The standard close-to-close estimator annualises the sample standard deviation of daily log returns:

$$\sigma_{RV} = \sqrt{\frac{252}{n-1}\sum_{t=1}^{n}(r_t - \bar r)^2}, \qquad r_t = \ln\frac{S_t}{S_{t-1}}$$

The window matters: a 10-day estimate reacts quickly and is noisy, a one-year estimate is smooth and slow. Range-based estimators by Parkinson (1980), Garman and Klass (1980) and Yang and Zhang (2000) use the open, high and low as well and reach the same precision with fewer days.

Implied volatility. It is not computed from returns at all. It is the volatility input that makes a pricing model match an option's market price, and because it comes from what buyers pay, it includes a premium for risk. The VIX aggregates S&P 500 implied volatilities into one 30-day figure.

The premium. On average implied volatility has exceeded the volatility that followed. The difference, measured in variance,

$$\text{VRP} = \sigma_{IV}^2 - \sigma_{RV}^2$$

is the volatility risk premium. Carr and Wu (2009) measure it with synthetic variance swaps and find it negative for the buyer of variance on average; Bollerslev, Tauchen and Zhou (2009) show that it helps predict equity returns.

Worked Example

Ten daily log returns, in percent: +0.5, -0.8, +1.1, -0.3, +0.6, -1.2, +0.4, +0.9, -0.7, +0.2. Their mean is 0.07 and the sum of squared deviations is 5.441, so the sample variance is 5.441 / 9 ≈ 0.6046 and the daily standard deviation 0.78 percent. Annualised, realised volatility is 0.78 × √252 ≈ 12.34 percent. The average absolute daily move is only 0.67 percent, the gap the Rule of 16 warns about.

Now suppose 30-day implied volatility is 18 and a seller of 30-day variance has a vega notional of 100,000, which corresponds to a variance notional of 100,000 / (2 × 18) ≈ 2,778 per variance point, the convention of a variance swap. The seller's profit depends on realised volatility:

An undershoot of 7 volatility points earns about a third of what an overshoot of 12 points costs; the variance risk premium calculator runs other combinations.

This asymmetry is why the premium exists and why strategies that harvest it share a signature: steady gains punctuated by sharp losses.

When It Applies (and Limitations)

Realised estimates are noisy. With 21 daily returns the standard error of a volatility estimate is roughly 15 percent of its value, so a measured 12 could easily be 10 or 14. Comparisons with implied volatility need windows that match the option's horizon and allowance for that noise.

The comparison must be forward-looking. Implied volatility today should be compared with the volatility realised over the option's remaining life, not with the past month. Comparing it with trailing realised volatility is a common shortcut and a different, weaker signal.

Jumps and gaps matter. Close-to-close estimators miss intraday swings, and overnight gaps around earnings or macro events can dominate realised variance. The premium is partly compensation for exactly these jumps.

The premium is not constant. It tends to widen after volatility spikes and can turn sharply negative during crises, when realised volatility overshoots what was priced. It also differs by asset: Carr and Wu find it much larger for equity indices than for most single stocks, because index options carry the market's demand for crash protection.

Why It Matters for Institutional Investors

Strategy design. Whether a strategy is long or short the volatility risk premium determines how it behaves in a crisis. Covered calls, short straddles, iron condors and variance selling collect it and lose in sudden selloffs; gamma scalping and tail hedges pay it and gain when realised volatility overshoots.

Hedging cost. The price of a protective put is set by implied volatility. Buying protection when implied volatility is already well above realised volatility is expensive insurance; the gap shows how expensive.

Due diligence. Smooth returns from a volatility strategy prompt two questions: is the strategy long or short the premium, and what did it lose when realised volatility spiked? A high Sharpe ratio earned by selling implied volatility is compensation for warehousing tail risk, and such strategies are better judged by their worst month than by their average.

Risk measurement. Realised volatility feeds risk models, position sizing and value at risk; implied volatility gives a forward-looking alternative. Using both, and watching the spread, separates what the market has done from what it is paying to avoid.

References

1. Carr, P., & Wu, L. (2009). Variance Risk Premiums. Review of Financial Studies, 22(3), 1311-1341.
2. Bollerslev, T., Tauchen, G., & Zhou, H. (2009). Expected Stock Returns and Variance Risk Premia. Review of Financial Studies, 22(11), 4463-4492.
3. Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business, 53(1), 61-65.
4. Garman, M. B., & Klass, M. J. (1980). On the Estimation of Security Price Volatilities from Historical Data. Journal of Business, 53(1), 67-78.
5. Yang, D., & Zhang, Q. (2000). Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices. Journal of Business, 73(3), 477-491.
6. Sinclair, E. (2013). Volatility Trading (2nd ed.). Wiley.