Implied Volatility Compared With Realised Volatility

Implied volatility is a market price for future variance, and realised volatility is what the underlying actually delivered, with the gap between them driving every relative-value volatility trade.

Implied volatility is the number that, fed into an option pricing model alongside the strike, expiry, spot and rate, reproduces the option's traded price. Realised volatility is the standard deviation of the underlying's own returns over a period that has already happened, annualised so it can be compared on the same scale. The distance between the two numbers, not either number in isolation, is what a volatility desk actually trades.

An option's implied volatility comes from inverting the pricing formula: given the market price of a call or put, solve for the volatility input that makes the model output match it. Because every strike and every expiry on the same underlying trades at its own price, each one implies its own volatility, and the full set across strikes and maturities is what desks call the volatility surface, covered from the skew side in why the volatility smile exists. A single number quoted as the implied volatility of a stock is almost always the at-the-money level for one specific expiry, a convenient summary rather than the whole picture.

Because implied volatility is backed out of a price, it reflects everything the market is currently willing to pay for, including supply and demand for hedges, dealer positioning and event risk, not a statistical view alone of how much the underlying is likely to move. A stock with an earnings release nine days out will show a step up in implied volatility for the expiry spanning that release, even if the stock has traded quietly for months beforehand.

Realised volatility is computed from the underlying’s own price history. The standard method takes the log return between each pair of consecutive closes over a chosen window, computes the standard deviation of those returns, and annualises by multiplying by the square root of 252, the approximate number of trading days in a year. If the daily log returns over the past 20 trading days have a standard deviation of 0.9 percent, annualised realised volatility works out to roughly 0.9 times 15.9, or about 14.3 percent.

The answer depends on the window length and the sampling frequency chosen, which is why a 10-day realised number and a 60-day realised number on the same stock can differ meaningfully even though both are correct measurements of something real. Estimators that use the high, low, open and close rather than only the close reduce that sampling error further, which matters when a trade depends on getting the forecast right to within a point or two.