Implied and realized volatility

Two readings of the same uncertain future

Implied volatility is the volatility input that makes an option-pricing model agree with an observed market price. Every strike and expiration can carry its own value, producing a curve across time and a surface across both time and strike.

Realized volatility, also called historical volatility, is calculated from changes in the underlying price. Vega commonly shows 20-session realized volatility beside 30-calendar-day implied volatility. The windows are close enough for a quick regime check, and their labels remain visible so the comparison has context.

How realized volatility is calculated

Start with daily log returns, calculate their sample standard deviation, and annualize using the square root of the usual 252 market sessions. Corporate-action-adjusted prices keep splits and distributions from appearing as fictional market moves.

The annualized figure is a rate. A 20% reading does not predict a 20% move over the next year. Under a simple diffusion assumption, it corresponds to a one-day standard deviation near 20% divided by the square root of 252, or about 1.26%.

Compare volatility in variance space

A quick dashboard comparison can use IV minus HV in volatility points. Research that combines horizons or decomposes events should work in variance, which is volatility squared. Variance scales with time under common modeling assumptions.

The variance spread can be positive because option sellers demand compensation for jump risk, convexity, hedging costs, and difficult market states. It can turn negative when the underlying moves faster than the option market had priced.

Worked example: a six-point IV premium

Suppose a stock has 30-day ATM IV of 25%. Its last 20 daily returns have a standard deviation of 1.20%, which annualizes to about 19.0% because 1.20% x sqrt(252) = 19.0%. The screen therefore shows an IV minus HV premium of 6.0 volatility points.

In variance terms, the difference is 0.25^2 - 0.19^2 = 0.0264, or 264 annualized variance basis points. That figure describes a rich implied-versus-realized setup. A short-volatility position still needs a sensible horizon, clean quotes, adequate liquidity, and room for any scheduled event.

A practical Vega workflow

• Start in the volatility screener and rank the universe by IV30, HV20, or their spread.
• Open a symbol and inspect the IV versus realized chart. Check whether the gap is persistent, new, or tied to one turbulent week.
• Review the term structure and known earnings date before choosing an expiration.
• Build a defined position in the calculator and examine theta, vega, breakevens, and price scenarios.
• Use historical replay to see how comparable entry dates behaved with daily marks and executable-side assumptions.